A2 June 2020 Paper 1 Q3

3 The quadratic equation \(ax^2 + bx + c = 0\) \((a, b, c \in \mathbb{R})\) has real roots \(\alpha\) and \(\beta\).

One of the four statements below is incorrect.

Which statement is incorrect?

Tick (✓) one box. [1 mark]

• \(c = 0 \Rightarrow \alpha = 0 \text{ or } \beta = 0\)
• \(c = a \Rightarrow \alpha \text{ is the reciprocal of } \beta\)
• \(b \lt 0 \text{ and } c \lt 0 \Rightarrow \alpha \gt 0 \text{ and } \beta \gt 0\)
• \(b = 0 \Rightarrow \alpha = -\beta\)