Can someone tell me how to find the real and complex roots of this polynomial?

Question

anonymous · Answer

What polynomial?

anonymous · Answer

This one: $$x^4 - 41x^2 = -400$$

anonymous · Answer

Sorry, my internet is really slow.

anonymous · Answer

Any ideas?

dtan5457 · Answer

You can graph it and find the zeros.

dtan5457 · Answer

x^4-41x^2+400=0

See where it touches the x intercepts?

anonymous · Answer

But is there any way I can solve it through factoring? I have to show my work for it.

anonymous · Answer

Could I maybe split the 41x^2 into two numbers?

directrix · Answer

@RadioEdit 

Picking up from above, you asked if x^4-41x^2+400=0

will factor (over  the set of Integers, I assume).

Yes, it will.

Look for two numbers that multiply to 400 and add to -41.

Hint: When you factor x^4 - 41x^2 + 400 = 0, you should get two binomial factors, each of which is the difference of two squares.