How do I find the roots of this polynomial of degree $4$? I am studying for finals and in the review packet is shown this problem:
$$P(x)=2x^4 + 5x^3 + 5x^2 + 20x - 12$$
I don't know what to do, I have already tried looking in the textbook and Khan academy.

Simple factorisation solves your problem.
$$P(x)=2x^4+5x^3+5x^2+20x-12$$ $$=2x^4+5x^3-3x^2+8x^2+20x-12$$
$$=x^2(2x^2+5x-3)+4(2x^2+5x-3)$$ $$=(x^2+4)(2x^2+5x-3)$$ $$=(x^2+4)(2x-1)(x+3)$$
Hence the $4$ roots are $x=\frac{1}{2}$,$x=-3$,$x=2i$ and $x=-2i$.
Hope this helps.
