Question

three of zeroes of a fourth degree polynomial equation are 1,-1,2i. Write the equation for the function if f(0) = 8

Answer 1

$a(x-1)(x+1)(x-2i)(x+2i)=\\ a(x^2-1)(x^2+4)=\\ a(x^4+4x^2-x^2-4)=\\ a(x^4+3x^2-4)\\\\ a(0^4+3\cdot0^2-4)=8 a\cdot(-4)=8\\ a=-2\\\\ -2(x^4+3x^2-4)=\boxed{-2x^4-6x^2+8}$