Quadratic Equation Calculator (with Discriminant)

Free quadratic equation calculator for Grade 12 CAPS maths. Enter a, b and c to get the roots, the discriminant and the nature of the roots instantly.

Enter the coefficients of ax² + bx + c = 0 to see the discriminant, the nature of the roots and both solutions rounded to two decimals — exactly the way the NSC memo expects them. Use it to check your working rather than replace it: in the exam you must show the substitution into the formula to earn the method marks. The discriminant tells you the nature of the roots before you solve, which is exactly what 'nature of the roots' and 'for which values of k' questions test.

How it works

  • The calculator computes the discriminant Δ = b² − 4ac first.
  • If Δ > 0 there are two unequal real roots; Δ = 0 gives one real root; Δ < 0 gives non-real roots.
  • Roots are then evaluated with x = (−b ± √Δ) / 2a.
  • If Δ is a perfect square (and a, b and c are rational), the roots are rational; otherwise they are irrational.
  • Worked example: for 2x² − 3x − 5 = 0, Δ = (−3)² − 4(2)(−5) = 49, a perfect square, so the roots are real, rational and unequal: x = (3 ± 7)/4, giving x = 2.5 or x = −1.

Frequently asked questions

Does this calculator show the working?

It shows the discriminant, the nature of the roots and both root values. For the full step-by-step method marks, snap the question into the Snap&Learn AI solver.

What if a = 0?

The equation is then linear, not quadratic, and the calculator will tell you to solve bx + c = 0 instead.

How do I set out the answer in the exam?

Write the formula, substitute a, b and c with brackets around negative values, simplify the discriminant, then give both roots, rounded to two decimal places unless the question asks for surd form.

Can it solve an equation that is not in standard form?

Rearrange it first so that one side is zero. For example, x(x − 3) = 4 becomes x² − 3x − 4 = 0, so enter a = 1, b = −3 and c = −4.

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.