题干

已知二次函数图象的顶点坐标为(0,1),且过点(﹣1,
5
4
),直线y=kx+2与y轴相交于点P,与二次函数图象交于不同的两点A(x1,y1),B(x2,y2).

(注:在解题过程中,你也可以阅读后面的材料)

附:阅读材料

   任何一个一元二次方程的根与系数的关系为:两根的和等于一次项系数与二次项系数的比的相反数,两根的积等于常数项与二次项系数的比.

   即:设一元二次方程ax2+bx+c=0的两根为x1,x2

   则:x1+x2=﹣

b
a
,x1•x2=
c
a

   能灵活运用这种关系,有时可以使解题更为简单.

   例:不解方程,求方程x2﹣3x=15两根的和与积.

   解:原方程变为:x2﹣3x﹣15=0

∵一元二次方程的根与系数有关系:x1+x2=﹣

b
a
,x1•x2=
c
a

∴原方程两根之和=﹣

3
1
=3,两根之积= 15
1
=﹣15.

上一题 下一题 0.0难度 选择题 更新时间:2013-12-23 08:26:46

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