I have the roots of a n degree polynomial, supossing all of the roots have multiplicity 1, I can get the original polynomial by multiplying the following binomials: $(z-z_0)*(z-z_1)*...*(z-z_n)$ where $z_0,z_1,...,z_n$ are the roots of my polynomial. My question is: Is there a way in which I can calculate the coefficients of the resulting polynomial? So for example, if the result from the product of the n binomials result in: $a_n*z^n+a_{n-1}*z^{n-1}+...+a_0$ Is there a formula for the $a_n, a_{n-1},...a_0$ Preferably a compact formula so I can program it.
Thanks.