Algebra
Intermediate

Vieta's Formulas

Relates the roots of a quadratic to its coefficients.

Formula

x1+x2=−ba,x1x2=cax_1 + x_2 = -\frac{b}{a}, \quad x_1 x_2 = \frac{c}{a}

Variables

x_1, x_2Roots
a, b, cCoefficients

Example

For x² − 5x + 6 = 0: roots sum to 5 and multiply to 6 — they are 2 and 3.

Did You Know?

Vieta's formulas link a polynomial's roots to its coefficients without ever solving the equation.

rootsquadraticvieta