Vieta’s Formulas

Roots from coefficients

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• For $x^2 + bx + c$: sum of roots $= -b$, product $= c$.
• For $ax^2 + bx + c$: sum $= -b/a$, product $= c/a$.
• Vieta’s formulas reveal roots’ properties without solving.

Steps

1. Sum and product
2. Place the roots
3. Without solving
4. Build a quadratic
5. Vieta for a cubic
6. Sum of squares of roots