题目内容
已知关于x的一元二次x2-6x+k+1=0的两个实数根x1,x2,![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_ST/0.png)
A.8
B.-7
C.6
D.5
【答案】分析:根据一元二次ax2+bx+c=0(a≠0)根与系数的关系得到x1+x2=-
=6,x1•x2=
=k+1,然后把变形得
+
=
=
,从而得到关于k的方程,解方程即可.
解答:解:∵x1+x2=-
=6,x1•x2=
=k+1,
∴
+
=
=
,
而
,
∴
=1,
∴k=5.
故选D.
点评:本题考查了一元二次ax2+bx+c=0(a≠0)根与系数的关系:若方程的两实数根为x1,x2,则x1+x2=-
,x1•x2=
.
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_DA/0.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_DA/1.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_DA/2.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_DA/3.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_DA/4.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_DA/5.png)
解答:解:∵x1+x2=-
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_DA/6.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_DA/7.png)
∴
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_DA/8.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_DA/9.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_DA/10.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_DA/11.png)
而
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_DA/12.png)
∴
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_DA/13.png)
∴k=5.
故选D.
点评:本题考查了一元二次ax2+bx+c=0(a≠0)根与系数的关系:若方程的两实数根为x1,x2,则x1+x2=-
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_DA/14.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103200410170460871/SYS201311032004101704608006_DA/15.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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