factoring.school factoring.school
Sign in

The Discriminant

Calculating the Discriminant

Calculating the discriminant is a substitution problem, but signs and the order of operations matter. Square b before subtracting 4ac.

The discriminant formula

For ax² + bx + c = 0, use Δ = b² − 4ac. A negative b becomes positive when squared, but a negative c changes the sign of the product 4ac.

How to calculate Δ

  1. Identify a, b, and c with their signs.
  2. Calculate b².
  3. Calculate 4ac separately.
  4. Subtract: b² − 4ac.
  5. Simplify before interpreting the result.

Worked example

Calculate Δ for x² − 4x + 4 = 0

  1. a = 1, b = −4, c = 4
  2. b² = (−4)² = 16
  3. 4ac = 4(1)(4) = 16

Δ = 16 − 16 = 0.

Common mistakes

  • Treating (−4)² as −16.
  • Subtracting only 4a or 4c instead of 4ac.
  • Reading coefficients before putting the equation in standard form.
The Quadratic Discriminant What Does the Discriminant Mean?

Practice more

Build fluency with more factoring and quadratic questions, or create an account to track mastery and build a streak.

Choose practice Save your progress