Question

Given that x^2x-3 is a factor of f(x)= x^4+6x^3+2ax^2+bx-3a. find the value of a and b?

Answer 1

if x^2-3 =0 then
x= -sqrt{3} and sqrt{3}
f(sqrt{3})=9+18$\sqrt{3}$+6a+$\sqrt{3}$b-3a =0
f(-$\sqrt{3}$)=9-18$\sqrt{3}$+6a-$\sqrt{3}$-3a =0
a=-3
b=-18