Discriminant

Δ = b² − 4ac, tells you the nature of a quadratic's roots. CAPS Grade 12 definition, worked NSC example and related algebra practice.

Δ = b² − 4ac, tells you the nature of a quadratic's roots.

Definition

The discriminant is the expression b² − 4ac taken from the quadratic equation ax² + bx + c = 0. Its value tells you how many roots the equation has and whether they are real, equal or non-real, without solving the equation.

Worked example

For 2x² − 5x − 3 = 0: Δ = (−5)² − 4(2)(−3) = 49. Since 49 > 0 and is a perfect square, the roots are real, unequal and rational.

Where it appears in the exam

A short Paper 1 question: determine the nature of the roots of a quadratic, or find the values of k for which the roots are real, equal or non-real.

Step-by-step method

  1. Write the equation in standard form ax² + bx + c = 0.
  2. Identify a, b and c, including their signs.
  3. Calculate Δ = b² − 4ac.
  4. Interpret: Δ < 0 non-real; Δ = 0 real and equal; Δ > 0 real and unequal (rational if Δ is a perfect square).

Common mistake

Not rearranging into standard form first, which gives the wrong values of a, b and c.

Frequently asked questions

What does discriminant mean in Grade 12 Maths?

The discriminant is the expression b² − 4ac taken from the quadratic equation ax² + bx + c = 0. Its value tells you how many roots the equation has and whether they are real, equal or non-real, without solving the equation.

Which NSC paper tests discriminant?

Discriminant belongs to the Algebra section of CAPS Grade 12 Mathematics, which is examined in Paper 1.

How do I practise questions involving discriminant?

Snap a question that uses discriminant into the Snap&Learn AI solver, or work through the algebra topic guide and NSC past papers.

Snap&Learn gives South African Matric learners instant, CAPS-aligned, step-by-step Mathematics solutions. Snap or upload a question and the AI shows every method mark the way the NSC memo awards them. Your first three AI solutions are free.