Find the range of values of $p$ for which $y = x^2 - x - 2$ lies entirely above the line \(y = p

Question

Find the range of values of $p$ for which $y = x^2 - x - 2$ lies entirely above the line $y = p(x + 2)$.[4] Hence, deduce, without finding the discriminant, the number of intersection points when $p = 3$.

Accepted Answer

(a) $-9<p<-1$ (b) $2$ intersection points

2025 AHS PRELIMS P1 Q1

2025 AHS PRELIMS P1 Q1

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