How to find all zeros of a polynomial

Question

Let $$f(x) = x^4 - 3x^3 + 2x^2 - 7x - 11. $$ I want to find the roots of $f(x)$.

I know that there are $3$ or $1$ positive roots, $1$ negative root, and $2$ or $0$ imaginary roots but I can't figure out how to find the actual roots, please help...

thank you

Answer 1

The roots are not all that nice...there are two real roots, two imaginary roots:

From Wolfram Alpha:

Real roots:

Complex roots: