Generated by claude-sonnet-4-6 · 2026-06-15 10:31 · grounding rag
Model Answer
Comparing with $ax^2 + bx + c = 0$: here $a = 1$, $b = -2a$, $c = -(4b^2 - a^2)$.
Using the quadratic formula:
$$x = \frac{2a \pm \sqrt{4a^2 + 4(4b^2 - a^2)}}{2} = \frac{2a \pm \sqrt{4a^2 + 16b^2 - 4a^2}}{2} = \frac{2a \pm \sqrt{16b^2}}{2} = \frac{2a \pm 4b}{2}$$
$$\therefore\quad x = a + 2b \quad \text{or} \quad x = a - 2b$$
Source: Chapter 4, Section 4.4
---
Explanation
- The key step is computing the discriminant: $(-2a)^2 - 4(1)(-(4b^2 - a^2)) = 4a^2 + 16b^2 - 4a^2 = 16b^2$, whose square root is simply $4b$.
- Examiners expect you to clearly show the discriminant calculation and then apply the formula — don't skip steps.
- Note: in this equation, the coefficient of $x^2$ is 1 (numeric), while $a$ and $b$ in the equation are parameters (not the standard $a, b, c$ of the formula) — be careful not to confuse them.