CAIE A-Level Mathematics AS 1.1.2 Quadratic Discriminant Questions

Practise forming b² − 4ac after rearranging to quadratic form and solving parameter inequalities for two distinct, one repeated or no real roots.

Exam points

solve quadratic equations using appropriate methods
analyse roots, discriminants and intersections
interpret quadratic functions in context

[Maximum number: 1]

Hence or otherwise find the set of values of p for which the equation $4 x^{2}-24 x+p=0$ has no real roots.

p-36>0 leading to p>36 or $24^{2}-4 \times 4 p\langle 0 \Rightarrow p\rangle 36$ or 36<p
Marking guidance:

Allow $(36, \infty)$ or $36<p<\infty$ . Consider final answer only.

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CAIE A-Level Mathematics AS 1.1.2 Quadratic Discriminant Questions question 1