Grade 11 · Theory
The discriminant
Quadratics · about 3 min
The discriminant predicts the roots before you solve.The discriminant Δ = b² − 4ac tells you about the roots without solving the equation.
Key points- Δ > 0: two different real roots (the graph cuts the x-axis twice).
- Δ = 0: one real root, repeated (the graph touches the x-axis).
- Δ < 0: no real roots (the graph misses the x-axis).
- Δ a perfect square means the roots are rational, so the quadratic factorises.
- Discriminant — the expression under the square-root sign.
- Real roots — solutions that exist on the number line.
EXAM TIP
"for which values of k will the roots be equal?" means set Δ = 0 and solve for k.