Question

已知二次函数y=x^2+bx+3的图象与x轴有两个交点,且这两个交点间的距离为2求b的值

Answer 1

x1+x2=-b

x1*x2=3

|x1-x2|=2

(x1+x2)^2

=(x1)^2+(x2)^2+2x1x2

=(x1-x2)^2+4x1x2

=4+12

=16

解得x1+x2=4或者-4

因此b=-4或者b=4