Free Linear and Quadratic Equations and Inequalities MCQs with Answers
30 Linear and Quadratic Equations and Inequalities MCQs from Quantitative Methods, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Linear equations are solved using algebraic manipulation, while quadratic equations involve factorisation, the quadratic formula, completing the square and the discriminant. Inequalities require careful treatment of solution intervals and reversal of the sign when multiplying or dividing by a negative number, unlike ordinary equation solving.
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30 questions · page 2 of 2
- A. x = 6
- B. x = 10
- C. x = 8
- D. x = 12
Explanation: Expanding gives 5x − 10 − 2x − 2 = x + 4, so 3x − 12 = x + 4. Therefore, 2x = 16 and x = 8.
Correct answer: x = 8- A. x = 10
- B. x = 12
- C. x = 16
- D. x = 14
Explanation: Multiplying the equation by 6 gives 4x − 2 − 3x − 6 = 6. Hence x − 8 = 6, so x = 14.
Correct answer: x = 14- A. k = 1 or 9
- B. k = 9 only
- C. k = 1 only
- D. k = −1 or −9
Explanation: Equal roots require the discriminant to be zero. Here, (k − 3)² − 4k = k² − 10k + 9 = (k − 1)(k − 9), giving k = 1 or k = 9.
Correct answer: k = 1 or 9- A. −4
- B. −2
- C. 2
- D. 4
Explanation: For ax² + bx + c = 0, the product of the roots is c/a. Thus, the product is −4/2 = −2.
Correct answer: −2- A. x = 2
- B. x = 4
- C. x = 3
- D. x = 6
Explanation: For y = ax² + bx + c, the vertex occurs at x = −b/(2a). Therefore, x = −6/(2 × −1) = 3, where the downward-opening parabola reaches its…
Correct answer: x = 3- A. x < −1/2 or x > 2
- B. −2 < x < 1/2
- C. x ≤ −1/2 or x ≥ 2
- D. −1/2 < x < 2
Explanation: The expression factors as (2x + 1)(x − 2). Since the parabola opens upward, it is negative strictly between its roots, so −1/2 < x < 2.
Correct answer: −1/2 < x < 2- A. x ≤ −8 or x ≥ 2
- B. −8 ≤ x ≤ 2
- C. x < −8 or x > 2
- D. −2 ≤ x ≤ 8
Explanation: An absolute value of at least 5 means x + 3 ≤ −5 or x + 3 ≥ 5. These conditions give x ≤ −8 or x ≥ 2, including both endpoints.
Correct answer: x ≤ −8 or x ≥ 2- A. a = −1
- B. a = 1
- C. a = 0
- D. a = 4
Explanation: When a = 1, the equation becomes 0x = 4, which is impossible and therefore has no solution.
Correct answer: a = 1- A. 9 cm
- B. 12 cm
- C. 15 cm
- D. 18 cm
Explanation: Let the width be w, so the length is w + 3. The perimeter equation is 2w + 2(w + 3) = 54, which gives 4w = 48 and w = 12 cm.
Correct answer: 12 cm- A. x = 3 only
- B. x = −3 only
- C. x = −1 or 1
- D. x = −3 or 3
Explanation: Set t = |x|, where t is nonnegative. Then t² − 2t − 3 = (t − 3)(t + 1) = 0, so t = 3 and therefore x = −3 or x = 3.
Correct answer: x = −3 or 3