对关于x的二次三项式-(2a^2+2a)x^2+(7a+3)x-6分解因式为?

Question

对关于x的二次三项式-(2a^2+2a)x^2+(7a+3)x-6分解因式为?

Answer 1

-(2a^2+2a)x^2+(7a+3)x-6
令-(2a^2+2a)x^2+(7a+3)x-6=0
△=(7a+3)²+4(2a²+2a)(-6)=a²-6a+9=(a-3)²≥0
x=[-(7a+3)±√(a-3)²]/-2(2a²+2a)
x1,2=3/2a或2/(a+1)
因此
-(2a^2+2a)x^2+(7a+3)x-6
=-(2a^2+2a)(x-3/2a)[x-2/(a+1)]
=-2a(a+1)(x-3/2a)[x-2/(a+1)]
=(3-2ax)(ax+x-2)