Question

For the following polynomial, one zero is given. Find the remaining zeros.

f(x)=x^4+40x^2-441

-7i is a zero.

Answer 1

its good to know that complex zeros come in +- pairs so that should eat up another zero

Answer 2

if you know quadratic methods, the other 2 zeros can be determined by recognizing that this is a quadratic in disguise

Answer 3

\[x^4+40x^2-441\]
\[(x^2)^2+40(x^2)-441\]
\[u=x^2\]\[(u)^2+40(u)-441\]