SPM 2017 Add Maths Paper 1, Question 13Quadratic Functions

Solved on video in English and Bahasa Melayu · 4 marks · Form 4, Quadratic Functions · 4:20 video

The question

(a) It is given that one of the roots of the quadratic equation x² + (p+3)x - p² = 0, where p is a constant, is negative of the other. Find the value of the product of roots. (b) It is given that the quadratic equation mx² - 5nx + 4m = 0, where m and n are constants, has two equal roots. Find m : n.

[4 marks]

SPM 2017 Add Maths Paper 1, Question 13: the question as drawn in Eduly's video4:20

Step 1

Let the roots be alpha and -alpha. Sum of roots = alpha + (-alpha) = 0. For x²+(p+3)x-p²=0, sum of roots = -(p+3)/1, so -(p+3) = 0, giving p = -3.

Why this step

α and −α cancel, so their sum is 0. That's why we use the sum of roots to find p. Using the product is a common slip.

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

Final answer

(a) −9; (b) m : n = 5 : 4

Where students lose marks

Watch out: find p in (a) using the sum of roots, not the product. In (b), take the square root: 5:4, not 25:16.

Watch every step of this question solved on video (4:20), with the reason behind each step and a box that checks your own answer.

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