Sum/Product of the Roots

For a polynomial $p_n(x) = a_nx^n + a_{n-1}x^{n-1} + \dots + a_1x + a_0 = 0$, Vieta's formulas describe the relationship between the coefficients and the sums and products of its roots.

• Sum of the roots: $-\frac{a_{n-1}}{a_n}$
• Sum of the products of the roots taken two at a time: $\frac{a_{n-2}}{a_n}$
• Product of the roots: $(-1)^n \frac{a_0}{a_n}$

For a quadratic $ax^2+bx+c=0$, the sum of roots is $-b/a$ and the product is $c/a$. For a cubic $ax^3+bx^2+cx+d=0$, the sum of roots is $-b/a$, the sum of roots taken two at a time is $c/a$, and the product is $-d/a$.