NUST NET Maths chapter 3: Maths · Quadratic equations MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

14 exam-style questions on Maths · Quadratic equations, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

14 questions · 1 topics · 10 per test

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What chapter 3 covers

Ten Maths · Quadratic equations questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. α and β are the roots of 2x2 + 5x − 3 = 0. The equation whose roots are 1/α and 1/β is

  1. A
    3x2 + 5x − 2 = 0
  2. B
    3x2 − 5x − 2 = 0
  3. C
    2x2 − 5x + 3 = 0
  4. D
    3x2 − 5x + 2 = 0
Show answer

Answer: B. Replace x by 1/x and clear fractions: 2 + 5x − 3x2 = 0, i.e. 3x2 − 5x − 2 = 0. Check: the original roots are 1/2 and −3, and (3x + 1)(x − 2) = 0 gives 2 and −1/3.

2. The roots of 2x2 − 4x + 3 = 0 are

  1. A
    real and equal
  2. B
    real, rational and unequal
  3. C
    real, irrational and unequal
  4. D
    imaginary (complex conjugates)
Show answer

Answer: D. The discriminant b2 − 4ac = 16 − 24 = −8 is negative, so the roots are non-real and form a conjugate pair.

3. If α and β are the roots of x2 − 5x + 3 = 0, then α2β + αβ2 is

  1. A
    −15
  2. B
    8
  3. C
    15
  4. D
    19
Show answer

Answer: C. α2β + αβ2 = αβ(α + β) = 3 × 5 = 15, using α + β = 5 and αβ = 3. Taking α + β = −5 (the sign slip in −b/a) gives −15.

4. The roots of 3x2 − 5x − 2 = 0 are

  1. A
    −2 and 1/3
  2. B
    2 and 1/3
  3. C
    3 and −2
  4. D
    2 and −1/3
Show answer

Answer: D. Factorise: 3x2 − 5x − 2 = (3x + 1)(x − 2), so x = 2 or x = −1/3. Check: the sum 2 − 1/3 = 5/3 = −b/a.

5. The roots of x2 − 6x + 7 = 0 are

  1. A
    real, rational and unequal
  2. B
    real, irrational and unequal
  3. C
    real and equal
  4. D
    imaginary (complex conjugates)
Show answer

Answer: B. The discriminant 36 − 28 = 8 is positive but not a perfect square, so the roots (3 ± √2) are real, unequal and irrational.

6. The real solutions of (x + 1)(x + 2)(x + 3)(x + 4) = 24 are

  1. A
    0 and 5
  2. B
    −1 and −4
  3. C
    1 and −6
  4. D
    0 and −5
Show answer

Answer: D. Pair the outer and inner factors: (x2 + 5x + 4)(x2 + 5x + 6) = 24. With y = x2 + 5x this is y2 + 10y = 0, so y = 0 (x = 0 or −5) or y = −10, and x2 + 5x + 10 = 0 has no real roots.

7. The roots of x2 − (√3 + 1)x + √3 = 0 are

  1. A
    1 and √3
  2. B
    −1 and −√3
  3. C
    1 and −√3
  4. D
    −1 and √3
Show answer

Answer: A. Two numbers with sum √3 + 1 and product √3 are 1 and √3, so the equation is (x − 1)(x − √3) = 0. Negative roots would make the sum negative.

8. The solutions of x1/2 − 5x1/4 + 6 = 0 are

  1. A
    4 and 9
  2. B
    2 and 3
  3. C
    16 and 81
  4. D
    8 and 27
Show answer

Answer: C. Let y = x1/4; then y2 − 5y + 6 = 0 gives y = 2 or 3. So x = 24 = 16 or 34 = 81; 2 and 3 are the values of y, not x.

9. If ω is a complex cube root of unity, then (1 + ω2)4 is equal to

  1. A
    ω
  2. B
    ω2
  3. C
    −ω
  4. D
    1
Show answer

Answer: A. Since 1 + ω + ω2 = 0, 1 + ω2 = −ω. Then (−ω)4 = ω4 = ω3 · ω = ω.

10. The roots of x2 + 2x + 5 = 0 are

  1. A
    1 ± 2i
  2. B
    −1 ± 4i
  3. C
    −2 ± i
  4. D
    −1 ± 2i
Show answer

Answer: D. x = [−2 ± √(4 − 20)]/2 = (−2 ± 4i)/2 = −1 ± 2i. Forgetting to halve the 4i gives −1 ± 4i.

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Ways to practise this chapter

Maths · Quadratic equations: questions students ask

How many Maths · Quadratic equations MCQs are there?

14, each with the answer and a short explanation, across 1 topics: Quadratic equations. Every chapter test draws ten of them, so you can take it many times.

Is the NUST NET Maths chapter 3 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

Can I read the explanations in Urdu?

Yes. In practice mode and on your results you can switch the explanations to Urdu.

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