Question

Help please!!

What are the real and complex solutions of the polynomial equation?
x^4-41x^2=-400

Answer 1

t=x^2

t^2-41t+400=0
t=16 or
t=25

if t=16 then x^2=16
x=4 or x=-4

if t=25 then x^2=25
x=5 or x=-5

Result: x=+-4 or +-5 - all solutions are real.

Answer 2

the complete factor of your polynomial is:
\[(x ^{2}-25)*(x ^{2}-16)\]
so you have to solve two quadratic equations

Answer 3

the answer of @AndreyZn is a good answer!