已知方程5x2+kx-10=0的一個(gè)根是-5,求它的另一個(gè)根及k的值.
【答案】
分析:根據(jù)根與系數(shù)的關(guān)系得到兩根之積=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202334576072659/SYS201311032023345760726017_DA/0.png)
=-2,可以算出另一根,然后利用兩根之和為-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202334576072659/SYS201311032023345760726017_DA/1.png)
可求得k.
解答:解:設(shè)方程的另一根是x
1,
那么-5x
1=-2,
∴
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202334576072659/SYS201311032023345760726017_DA/2.png)
.
又∵
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202334576072659/SYS201311032023345760726017_DA/3.png)
+(-5)=-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202334576072659/SYS201311032023345760726017_DA/4.png)
,
∴k=-5[
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202334576072659/SYS201311032023345760726017_DA/5.png)
+(-5)]=23.
答:方程的另一根是
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202334576072659/SYS201311032023345760726017_DA/6.png)
,k的值是23.
點(diǎn)評(píng):用到的知識(shí)點(diǎn)為:一元二次方程的兩根之和為-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202334576072659/SYS201311032023345760726017_DA/7.png)
,兩根之積為
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202334576072659/SYS201311032023345760726017_DA/8.png)
.