Question

实数M取何值时,关于X的方程X^2+(M-2)X-(M+3)=0的两根的平方和最小,并求该最小值.

Answer 1

X^2+(M-2)X-(M+3)=0

△=(m-2)^2+4(m+3)

=m^2-4m+4+4m+12

=m^2+16>0

x1+x2=2-m

x1x2=-(m+3)

x1^2+x2^2

=(x1+x2)^2-2x1x2

=4-4m+m^2+2m+6

=m^2+2m+10

=(m+1)^2+9

当 m=-1时

两根平方和最小为 9