Question

一个二次三项式的完全平方式是4x^4+12x^3-ax^2-bx+16,求a,b

Answer 1

令这个二次三项式是2*x^2+c*x+4==>(2*x^2+c*x+4)^2

=4*x^4+4c*x^3+(16+c^2)*x^2+8c*x+16

=4*x^4+12*x^3+ a*x^2 -b*x +16

==>4c=12==>c=3;a=16+c^2==>a=25;b=8c=24