The discriminant trick that catches out A-Level students

Published 2026-03-11 · Written by Pete Bromfield

You've seen the discriminant a hundred times. It's just $b^2 - 4ac$. And yet at Edexcel A-Level, the discriminant question in Paper 1 routinely costs strong students a full 3 marks. This post walks through why.

The three cases — in one line

• $b^2 - 4ac > 0$ — two distinct real roots.
• $b^2 - 4ac = 0$ — one repeated root (also called equal roots).
• $b^2 - 4ac < 0$ — no real roots.

The typical Paper 1 question

The equation $x^2 - (k + 3)x + 4 = 0$ has two distinct real roots. Find the range of values of $k$.

Setting $a = 1$, $b = -(k+3)$, $c = 4$, we need $b^2 - 4ac > 0$, so $(k+3)^2 - 16 > 0$, so $(k+3)^2 > 16$, so $k + 3 > 4$ or $k + 3 < -4$, i.e. $\boxed{k > 1 \text{ or } k < -7}$.

The three ways students lose the marks

1. Writing the strict inequality as $\geq$ instead of $>$ (which would include the repeated-root case).
2. Solving $(k+3)^2 > 16$ as $k + 3 > 4$ only, forgetting the negative branch.
3. Sign errors squaring $-(k+3)$. Always add brackets before you square.

Now drill 10 of these back-to-back on Skills Practice. Your Paper 1 marks will thank you.