Quadratic Discriminant

Free interactive math game: Quadratic Discriminant — How many real roots?. Part of the Functions category on MathKite.

Example problems

Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.

  1. How many real solutions has: 2x² + 6x − 6 = 0 ?
  2. How many real solutions has: 2x² − 2x − 2 = 0 ?
  3. How many real solutions has: 3x² + 6x + 5 = 0 ?
  4. How many real solutions has: x² = 0 ?

About this exercise

The discriminant, which counts the solutions of a quadratic.

How to solve it

Work out b squared minus 4ac. Positive gives two roots, zero gives one, and negative gives none.

Worked example

For x squared + 2x + 1, the discriminant is 4 - 4 = 0, so there is one root.

Common mistake

Losing a sign when a or c is negative. That flips the whole result.