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【331016】4.6 一元二次方程根与系数的关系 同步练习2

时间:2025-01-21 13:30:59 作者: 字数:4999字
简介:

4.6 一元二次方程根与系数的关系

同步练习

一、选择题

1.若 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> 是一元二次方程 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> 的两个根,则 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> 的值是( )

A2 B1 C.―1 D3

2.若关于x的一元二次方程 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> 的两个实数根分别是 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> ,且满足 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> .k的值为(  )

A.-1 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>   B.-1  C <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>   D.不存在

3方程x2-3x-6=0与方程x2-6x+3=0的所有根的乘积为( )

A-18 B18 C-3 D3

4x1x2是一元二次方程2x2-3x+1=0的两个根,则x12+x22 的值是( )

A <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> B <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> C <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> D7

5.若关于x的一元二次方程2x22x3m10的两个实数根x1x2,且x1·x2x1x24,则实数m的取值范围是( )

Am <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> Bm≤ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> Cm <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> D <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>m≤ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>

5.已知方程x2+(2k+1)x+k22=0的两实根的平方和等于11k的取值是( )

A3 B.-3 C1 D.-31

6下列说法中不正确的是( )

A方程x2+2x-7=0的两实数根之和为-2

B方程x2-3x-5=0的两实数根之积为-5

C方程x2-2x-7=0的两实数根的平方和为18

D.方程x2-3x-5=0的两实数根的倒数和为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>

7.如果x的方程x2+kx+1=0的两根的差为1,那么k的值为( )

A±2 B± <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> C± <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> D± <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>

8已知关于x的方程5x2+kx-6=0的一个根为2,设方程的另一个根为x1,则有( )

Ax1= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> k=-7 Bx1=- <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> k=-7 Cx1=- <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> k=7 Dx1= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> k=7

二、填空题

1.已知一元二次方程 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> 的两根为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> ,则 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>  

2.如果 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> 是方程 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> 的两个根,那么 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>

3.已知 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> 是方程 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> 的两实数根,则 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> 的值为______

4.已知 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> 是关于 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> 的方程 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> 的两个实数根,且 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> ,则 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>

5x1x2是方程2x2+4x-3=0的两个根,则(x1+1)(x2+1)=

6.若方程 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> 的两根为aβ,则 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>

7.若方程 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> 的两根之比是23,则k=

8请写出一个二次项系数为1,两实根之和为3的一元二次方程:

三、解答题

1.已知关于x的二次方程x2+mx-1=0的一个根是 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> ,求另一个根及m的值.




2.已知关于x的方程x2-(k+1x+k+2=0的两个实数根的平方和等于6,求k的值.





3αβ是关于x的一元二次方程(m1)x2x + 1 = 0的两个实数根,且满足(α+1)(β+1) = m +1,求实数m的值




4.已知关于x的方程 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> ,问:是否存在正实数m,使方程的两个实数根的平方和等于56,若存在,求出m的值;若不存在,请说明理由.










5已知关于x的一元二次方程x2+(4m+1)x+2m-1=O

(1)求证:不论m为任何实数,方程总有两个不相等的实数根;

(2)若方程两根为x1x2,且满足+ =-,求m的值.

















参考答案

一、选择题

1B2C3A4A5D6D

7B.〖提示〗令x1x2,因为x1+x2=-kx1x2=1,所以x1-x2=

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> =1,所以k2-2=1,所以k=± <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>

8B.提示:因为x1x2=- <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> ,所以2x1=- <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> ,所以x1=- <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> ,又x1+x2= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> ,所以k=5× <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>=-7

二、填空题

1 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>263104 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>5 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>

610738.答案不唯一,如x2-3x-2=0等;

三、解答题

1.设方程的另一个根为x1,那么( <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>·x1=1,所以x1= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>

又因为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> ,所以m=2.所以方程的另一个根为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>


2.设方程的两根 x1x2,则x1+x2=k+1x1x2=k+2.因为x12+x22=(x1+x2)2―2x1x2=6,即(k+1)22k+2=6,解之,得k=±3.当k=3时,△=(k+1)24k+2=424×50.当k=3时,△=(-2)24-1=80

所以k=3不合题意,舍去,故k=3


3.根据题意,得α+β= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> αβ= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> ,且m-1≠0

因为(α+1)(β+1) = m +1,所以αβ+α+β=m,所以 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> + <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> =m,所以m2-m-2=0,所以m1=2m2=1(不合题意,舍去).即实数m的值为2


4.设方程 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> 的两实数根是x1x2,假设存在正数m,使方程的两个实数根的平方和等于56,则x12+x22=56,所以(x1+x22-2x1x2=56,又因为x1+x2=2m-2),x1x2=m2, 所以4(m-2)2-2m2=56,所以m2-8m-20=0,所以m1=-8m2=10

因为m为正数,所以m=-8舍去

m=10时,原方程变形为x216x+100=0,该方程的△=-162-4×1000,与该方程有两个实数根相矛盾

所以不存在正数m,使方程的两个实数根的平方和等于56


5.(1)证明:因为一元二次方程x2+(4m+1)x+2m-1=O的根的判别式

=(4m+1)242m-1=16m2+8m+1-8m+4=16m2+5

因为不m取何值时,m2≥0,所以16m2+5总大于0,即不论m为任何实数,方程总有两个不相等的实数根;

2)因为方程两根为x1x2,所以x1+x2=-(4m+1),x1x2=2m1

因为+ =-,所以 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> ,所以 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a> ,所以m= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/151/" title="关系" class="c1" target="_blank">关系</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/897/" title="二次方程" class="c1" target="_blank">二次方程</a> <a href="/tags/922/" title="系数" class="c1" target="_blank">系数</a>