How can I compute all roots of an equation of any degree manually ( even if that eq. has complex roots )?

Question

Manually=by hand -> not using software like Matlab ex: put coef. in a vector v and then roots(v) to find out all the solutions

Answer 1

First, I'm guessing the equation is a polynomial. So try to factor the polynomial to the best of your ability. If you have all linear factors, just set each factor equal to zero and find its root. If you have a quadratic root, set it equal to zero and you may have a real or imaginary root. For every polynomial with degree n, there are either n, n-2, n-4, n-6, ....0 real roots but there are n total roots.

Answer 2

Manually? I assume this means algebraically, but alas, Abel showed that polynomials above the fifth degree cannot be solved by standard algebraic means.