Math Quadratic equations Vieta's formulas

Vieta's formulas

Vieta's formulasis helpful when two of the four variables $p$, $q$, $x_1$ and $x_2$ are given and the other two are searched.



Vieta's formula may only be applied to quadratic equations in the canonical form (the $x^2$ in the equation is only multiplied by 1).

Given is a quadratic equation in the canonical form: $x^2+px+q=0$.
Vieta's formula says:

$q=x_1\cdot x_2$


Using Vieta's formula, construct a quadratic equation in the canonical form that has the solutions $x_1=-1$ and $x_2=-5$.

  1. Determine $p$ with Vieta's formula

  2. Determine $q$ with Vieta's formula

    $q=x_1\cdot x_2$
  3. Insert $p$ and $q$ in the canonical form