Vieta's formulas

Theorem 14.1.4 (Vieta’s Formula For Higher Degree Polynomials) In a polynomial with roots

the following holds:

$r_1 + r_2 + r_3 + \cdots + r_n (the sum of all terms) = −\frac{a_{n−1}}{a_n}$ (Error compiling LaTeX. Unknown error_msg) \\ $r_1r_2 + r_1r_3 + \cdots + r_{n−1}r_n (the sum of all products of 2 terms) = \frac{a_{n−2}}{a_n}$ (Error compiling LaTeX. Unknown error_msg) \\ $r_1r_2r_3 + r_1r_2r_4 + \cdots + r_{n−2}r_{n−1}r_n (the sum of all products of 3 terms) = −\frac{a_{n−3}{a_n}$ (Error compiling LaTeX. Unknown error_msg) \\

$r_1r_2r_3 \cdots r_n (the sum of all products of n terms) = (−1)^n \frac{a_0}{a_n}$ (Error compiling LaTeX. Unknown error_msg)

Note that the negative and positive signs alternate. When summing the products for odd number of terms, we will have a negative sign otherwise we will have a positive sign.