I have a question about Viete's formulas If I have a polynomial $a_n x^n + a_{n-1}x^{n-1}+ \cdots + a_1 x + a_0$, and the roots of the polynomial is $r_1,r_2,\ldots,r_n$, then I can rewrite the polynomial as,
$a_n x^n + a_{n-1}x^{n-1}  \cdots + a_1 x + a_0 = (x-r_1)\cdots(x-r_n)$. Now if I wanted to express each coefficient of the polynomial by its roots, how would I go about that?
For example, is $a_0 = (-1)^n(r_1\cdots r_n)$? What about $a_1,a_2,\ldots,a_n$?
Would $a_1 = (-1)^{n-1}(r_1 r_2\cdots r_{n-1} + r_1 r_2\cdots r_{n-2} r_n + \cdots)$?

The answer to both questions is yes, provided that $a_n=1$.
