Vieta's theorem

Vieta's theorem generalizes to polynomials of any degree. For a quadratic $ax^2 + bx + c = 0$ with roots $r$ and $s$:

• $r + s = -\frac{b}{a}$
• $rs = \frac{c}{a}$ For a cubic $ax^3 + bx^2 + cx + d = 0$ with roots $r$, $s$, $t$:
• $r + s + t = -\frac{b}{a}$
• $rs + rt + st = \frac{c}{a}$
• $rst = -\frac{d}{a}$

Important properties

• Relates sums and products of roots to coefficients

• Works for polynomials of any degree

• Can be used to construct polynomials with given roots