Question

If 2i is a zero of f(x)=x^4+x^2+a, find the value of a

Answer 1

By the polynomial remainder theorem, because x = 2i is a zero of f(x), we have no remainder upon dividing f(x) by x - 2i.

Computing the quotient yields

$\dfrac{x^4+x^2+a}{x-2i} = x^3+2ix^2-3x-6i+\dfrac{12+a}{x-2i}$

Then if the remainder term is 0, follows that a = -12.