Question

已知m,n是方程2x^2-3x-1=0的两个实数根,则2m^2-2m+mn+n的值是多少？

Answer 1

m+n=-(-3)/2=3/2
mn=-1/2
2m^2-2m+mn+n
=2m^2-2m-1/2+3/2-m
=(m-1)(2m-1)
=(m-1)(2-2n)
=-2(mn-m-n+1)
=-2(-1/2-3/2+1)
=2