方程X^2+(2M+1)X+M^2-2=0的两根平方和等于11,求M.

题目

方程X^2+(2M+1)X+M^2-2=0的两根平方和等于11,求M.
___are needed.A.other two B.two else C.two more D.the other two

答案

设两根分别为x1,x2,由韦达定理得
x1+x2=-(2m+1)
x1x2=m^2 -2
x1^2+x2^2=(x1+x2)^2-2x1x2
=[-(2m+1)]^2-2(m^2-2)
=4m^2+4m+1-2m^2+4
=2m^2+4m+5=11
2m^2+4m-6=0
m^2+2m-3=0
(m+3)(m-1)=0
m=-3或m=1
___are needed.A.other two B.two else C.two more D.the other two
选D