SPM 2022 Add Maths Paper 2, Question 3Quadratic Functions

Solved on video in English and Bahasa Melayu · 6 marks · Form 4, Quadratic Functions · 4:54 video

The question

(a)

A quadratic function is given by f(x) = 2x² − 5x + p, such that p is a constant.

(a) The roots of the quadratic equation when f(x) = 0 are α and β. Form a quadratic equation which has roots 2α − 1 and 2β − 1 in terms of p.

[3 marks]

(b)

Using f(x) = 2x² − 5x + p:

(b) Given that the straight line y = x + 1 touches the curve y = f(x), find the value of p.

[3 marks]

Step 1

For 2x² − 5x + p = 0: sum of roots α + β = −(−5)/2 = 5/2, product of roots αβ = p/2.

Why this step

Solving for α and β would be messy with p unknown. Vieta gives their sum and product straight from the coefficients, no solving needed.

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

Final answer

x² − 3x + (2p − 4) = 0

Where students lose marks

Watch out: keep the original sum 5/2 and the new sum 3 apart. The new product uses α + β = 5/2.

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

Final answer

p = 11/2

Where students lose marks

Watch out: touching means b² − 4ac = 0 on the combined equation. Don't use the quadratic formula to find p.

Watch every step of this question solved on video (4:54), with the reason behind each step and a box that checks your own answer.

No card. Every past-year question on video, in English and BM.