FSc Part 1 Maths chapter 4: Quadratic equations MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

29 exam-style questions on 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.

29 questions · 3 topics · 10 per test

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What chapter 4 covers

Ten 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. For the equation ax2 + bx + c = 0 (a ≠ 0), the quadratic formula is

  1. A
    x = (−b ± √(b2 − 4ac))/a
  2. B
    x = (b ± √(b2 − 4ac))/2a
  3. C
    x = (−b ± √(b2 + 4ac))/2a
  4. D
    x = (−b ± √(b2 − 4ac))/2a
Show answer

Answer: D. Completing the square on ax2 + bx + c = 0 gives x = (−b ± √(b2 − 4ac))/2a. Watch the −b and the 2a.

2. When x3 + 2x2 − 5x − 6 is divided by x − 2 using synthetic division, the quotient is

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

Answer: D. Coefficients 1, 2, −5, −6 with 2: bring down 1; 2 + 2 = 4; −5 + 8 = 3; −6 + 6 = 0. Quotient x2 + 4x + 3, remainder 0.

3. The product of the three cube roots of unity is

  1. A
    ω
  2. B
    0
  3. C
    −1
  4. D
    1
Show answer

Answer: D. 1 × ω × ω2 = ω3 = 1. It is their sum that equals 0.

4. The roots of x2 + x + 1 = 0 are

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

Answer: A. Discriminant b2 − 4ac = 1 − 4 = −3 < 0, so the roots are a pair of complex conjugates.

5. The quadratic equation whose roots are 3 and −5 is

  1. A
    x2 + 8x + 15 = 0
  2. B
    x2 − 2x − 15 = 0
  3. C
    x2 + 2x − 15 = 0
  4. D
    x2 − 2x + 15 = 0
Show answer

Answer: C. x2 − (sum)x + product = 0 with sum −2 and product −15: x2 + 2x − 15 = 0.

6. The product of the four fourth roots of unity is

  1. A
    i
  2. B
    1
  3. C
    0
  4. D
    −1
Show answer

Answer: D. 1 × (−1) × i × (−i) = (−1)(−i2) = (−1)(1) = −1. Many students assume every product of roots of unity is 1.

7. The remainder when x3 − 2x2 + 4 is divided by x − 2 is

  1. A
    −12
  2. B
    4
  3. C
    0
  4. D
    8
Show answer

Answer: B. By the remainder theorem the remainder is f(2) = 8 − 8 + 4 = 4. Using f(−2) = −12 is the sign slip.

8. The roots of x2 − 5x + 6 = 0 are

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

Answer: D. x2 − 5x + 6 = (x − 2)(x − 3), so x = 2 or 3. The factors must multiply to +6 and add to −5.

9. The solutions of the reciprocal equation x + 1/x = 5/2 are

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

Answer: D. Multiply by 2x: 2x2 − 5x + 2 = 0, so (2x − 1)(x − 2) = 0 and x = 2 or 1/2. Check: 2 + 1/2 = 5/2.

10. The roots of x2 − 4x + 1 = 0 are

  1. A
    2 ± √3
  2. B
    −2 ± √3
  3. C
    4 ± √3
  4. D
    2 ± √5
Show answer

Answer: A. x = (4 ± √(16 − 4))/2 = (4 ± √12)/2 = (4 ± 2√3)/2 = 2 ± √3. Using b2 + 4ac gives √20 and the wrong answer 2 ± √5.

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Ways to practise this chapter

Quadratic equations: questions students ask

How many Quadratic equations MCQs are there?

29, each with the answer and a short explanation, across 3 topics: Solving quadratic and reducible equations, Roots of unity and polynomial theorems, Roots, coefficients and nature of roots. Every chapter test draws ten of them, so you can take it many times.

Is the FSc Part 1 Maths chapter 4 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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