MRSM Trial 2025 Add Maths Paper 1, Question 7Quadratic Functions

Solved on video in English · Form 4, Quadratic Functions · 9:29 video

The question

(a)

A quadratic equation is given by x² + 9x + 2k = 0, such that k is a constant. It is given that the equation has roots α and β. Form a quadratic equation with roots 2 + α − β and 2 − α + β in terms of k.

(b)

Find the range of values of p for the inequality 2p² ≥ 13p + 7 by using the graph sketching method.

(c)

A quadratic equation is given by 6x² + 3x = 8x − q, such that q is a constant. Find the range of values of q if the equation has real roots.

MRSM Trial 2025 Add Maths Paper 1, Question 7: the question as drawn in Eduly's video9:29

Part (a)

Step 1

From x² + 9x + 2k = 0: sum of roots α + β = −9, product αβ = 2k.

Why this step

We never need α and β themselves. Their sum and product are enough to rebuild a new quadratic, so we grab those first.

5 more steps, each with the reason for it, in the full solution

Final answer

x² − 4x + 8k − 77 = 0

Where students lose marks

Watch out: use (α − β)² = (α + β)² − 4αβ, and mind the signs: 4 − (81 − 8k) = 8k − 77.

Part (b)

5 more steps, each with the reason for it, in the full solution

Final answer

p ≤ −1/2 or p ≥ 7

Where students lose marks

Watch out: for an upward parabola and ≥ 0, take the outside region (p ≤ −1/2 or p ≥ 7), not the inside one.

Part (c)

4 more steps, each with the reason for it, in the full solution

Final answer

q ≤ 25/24

Where students lose marks

Watch out: move every term to one side first, so b = −5, not 3. Real roots means b² − 4ac ≥ 0.

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