SPM 2019 Add Maths Paper 1, Question 9Quadratic Functions

Solved on video in English and Bahasa Melayu · 3 marks · Form 4, Quadratic Functions · 5:49 video

The question

It is given that the quadratic equation (px)² + 5qx + 4 = 0 has two equal roots while the quadratic equation hx² - x + p = 0 has no roots, where p, q and h are constants. Express the range of q in terms of h.

[3 marks]

SPM 2019 Add Maths Paper 1, Question 9: the question as drawn in Eduly's video5:49

Step 1

(px)²+5qx+4=0 is p²x²+5qx+4=0. Two equal roots means discriminant = 0: (5q)² - 4(p²(4) = 0.

Why this step

Two equal roots means the graph just touches the x-axis once, so the discriminant is 0. Careful: (px)² = p²x², so a = p², not p.

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

Final answer

q > 1/(5h) if h > 0; q < 1/(5h) if h < 0

Where students lose marks

Watch out: h could be positive or negative. Dividing by a negative flips the inequality, so give both cases, not just one.

Watch every step of this question solved on video (5:49), with the reason behind each step and a box that checks your own answer.

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