SPM 2020 Add Maths Paper 1, Question 5Quadratic Functions

Solved on video in English and Bahasa Melayu · 3 marks · Form 4, Quadratic Functions · 3:19 video

The question

Alpha and beta are the roots of the quadratic equation x² + px + q = 0, where p and q are constants. Alpha² and beta² are the roots of the quadratic equation x² - 3mx + q² = 0, where m is a constant. Express m in terms of p and q.

[3 marks]

SPM 2020 Add Maths Paper 1, Question 5: the question as drawn in Eduly's video3:19

Step 1

For x² + px + q = 0: sum of roots alpha + beta = -p; product alpha*beta = q.

Why this step

We can't solve for α and β because p and q are unknown. But the coefficients already give the sum and product of the roots, and that is all we need.

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

Final answer

m = (p² − 2q)/3

Where students lose marks

Watch out: α² + β² is not (α + β)². Remember to subtract 2αβ, or you lose the marks.

Watch every step of this question solved on video (3:19), with the reason behind each step and a box that checks your own answer.

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