Melaka Trial 2025 Add Maths Paper 1, Question 2Quadratic Functions

Solved on video in English · Form 4, Quadratic Functions · 5:47 video

The question

(a)

(a) Express the quadratic equation 3(3x + 4) = (x − 3)(x − 5) − x in the general form ax² + bx + c = 0. Hence, if α and β are the roots of the equation, state the value of α + β and αβ.

(b)

(b) Given that (x + h)² − j = 0 is a quadratic equation where h = 4 and j = 64. Determine the roots of the equation. [Note: the English paper asks to 'Determine the roots'; the Malay wording asks to determine the type/nature of the roots.]

Melaka Trial 2025 Add Maths Paper 1, Question 2: the question as drawn in Eduly's video

5:47

Part (a)

Step 1

Expand both sides: left side 3(3x + 4) = 9x + 12; right side (x − 3)(x − 5) − x = x² − 8x + 15 − x = x² − 9x + 15.

Why this step

The extra −x sits outside the brackets, so subtract it after expanding. Forgetting it, or expanding (x − 3)(x − 5) wrongly, is a common way to lose marks.

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

Final answer

x² − 18x + 3 = 0; α + β = 18; αβ = 3

Where students lose marks

Watch out: keep the extra −x when expanding, and use α + β = −b/a, so b = −18 gives +18, not −18.

Part (b)

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

Final answer

x = −12 or x = 4 (b² − 4ac = 256 > 0, two distinct real roots)

Where students lose marks

Watch out: expand (x + 4)² fully, and mind the signs when factorising: the roots are −12 and 4, not 12 and −4.

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Melaka Trial 2025 Add Maths Paper 1, Question 2Quadratic Functions

The question

Part (a)

Part (b)

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