Complex Zeros Question

Question

Find a polynomial with leading coefficient 1, degree 5, zeros i and , and passing through the origin. Simplify your answer so that it has only real numbers as coefficients. 

Answer 1

x ( x - i ) (x + i) [ ( x - 7) + i ] [ ( x - 7 ) - i ] =

x( x^2 + 1) [( x-7)^2 + 1 ] =

x ( x^2 + 1 ) (x ^2 - 14x + 50)