How can I design an algorithm for calculating n roots of a polynomial?

Question

I wish to make a C++ program to calculate n roots of a polynomial of n degree, and print them, even if they are real or complex...

I know that one can easily use quadratic formula for a quadratic equation, but are there formulas for other roots?

Is there a generalized way for an n degree polynomial using calculus or some other branch?

Or do there exist other formulas for this purpose (like for cubic, quartic, etc)?

Please help me, as I haven't encountered these topics in mathematics yet...

Thank You!

Answer 1

Good question...the link advises to "linearise the problem". If an initial value is too far off, the method might not converge. You might want to look into the Stochastic Funnel Algorithm to optimize the method.

Answer 2

You could use Newton's numerical method.

https://en.m.wikipedia.org/wiki/Newton%27s_method

Answer 3

@Karl T.
Thank You, Sir!

But I have a doubt...
How will I approximate the first root for the polynomial equation? //As, it can even be complex...

Answer 4

@Karl T.
Ill check more into that.
Thank You Sir!

Answer 5

Please do note that I can calculate some derivatives and integrals of expressions and complex functions using the symbolic c++ library I found a few days ago...