Free Quadratic Equations MCQs with Answers
28 Quadratic Equations MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Quadratic equations contain a squared variable and can be solved by factorisation, completing the square, the quadratic formula, or graphical reasoning. Questions cover roots, the discriminant, and the relationship between roots and coefficients, while distinguishing real and repeated roots from complex or non-real roots.
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28 questions · page 1 of 2
- A. 3 * 2.75 * 2.75 * 2.75
- B. 3 * 2.00 * 2.00 * 2.00
- C. 3 * 2.75 * 0.75 * 2.75
- D. 4.5 * 2.75
Explanation: Since 2.75 = 2.00 + 0.75, use a^3 - b^3 - c^3 = 3abc when a = b + c: 3 x 2.75 x 2.00 x 0.75 = 12.375.
Correct answer: 4.5 * 2.75- A. -6, 3
- B. 3, -2/3
- C. -5, 2
- D. -9, 2
Explanation: Factor the equation as 3x² - 7x - 6 = (3x + 2)(x - 3) = 0. Thus 3x + 2 = 0 gives x = -2/3, and x - 3 = 0 gives x = 3.
Correct answer: 3, -2/3- A. -6, 7
- B. -8, 7
- C. 14, -3
- D. -7, 6
Explanation: The quadratic factors as x² + x - 42 = (x + 7)(x - 6) = 0. Hence the roots are x = -7 and x = 6.
Correct answer: -7, 6- A. -2, -1/2
- B. 4, -1
- C. 4, 1
- D. -2, 5/2Election Officer Mcqs
Explanation: Factor 2x² + 5x + 2 as (2x + 1)(x + 2) = 0. The roots are x = -1/2 and x = -2, which are the two values listed in option a.
Correct answer: -2, -1/2- A. If a > b
- B. If a ≥ b
- C. If a < b
- D. If a ≤ b.
Explanation: For a² - 13a + 42 = 0, (a - 6)(a - 7) = 0, so a is 6 or 7. For b² - 15b + 56 = 0, (b - 7)(b - 8) = 0, so b is 7 or 8; in every pairing, a…
Correct answer: If a ≤ b.- A. If a > b
- B. If a ≥ b
- C. If a < b
- D. If a ≤ b
Explanation: Interpreting a3 as a³, a³ - 988 = 343 gives a³ = 1331, so a = 11. Also, b² - 72 = 49 gives b² = 121, so b = 11 or -11; therefore a ≥ b in…
Correct answer: If a ≥ b- A. If a > b
- B. If a ≥ b
- C. If a < b
- D. If a ≤ b
Explanation: For 9a² + 18a + 5 = 0, the roots are a = (-18 ± 12)/18, giving -1/3 and -5/3.
Correct answer: If a > b- A. If x < y
- B. If x > y
- C. If x ≤ y
- D. If x ≥ y
Explanation: Factoring gives x² + 11x + 30 = (x + 5)(x + 6), so x is -5 or -6. Similarly, y² + 15y + 56 = (y + 7)(y + 8), so y is -7 or -8; every…
Correct answer: If x > y9. I. x2 + 3x - 18 = 0, II. y2 + y - 30 = 0 to solve both the equations to find the values of x and y?
- A. If x < y
- B. If x > y
- C. If x ≤ y
- D. If x ≥ y
- E. If x = y or the relationship between x and y cannot be established.
Explanation: The first equation factors as (x + 6)(x - 3) = 0, giving x = -6 or 3. The second factors as (y + 6)(y - 5) = 0, giving y = -6 or 5, so x…
Correct answer: If x = y or the relationship between x and y cannot be established.10. I. x2 + 9x + 20 = 0, II. y2 + 5y + 6 = 0 to solve both the equations to find the values of x and y?
- A. If x < y
- B. If x > y
- C. If x ≤ y
- D. If x ≥ y
Explanation: x² + 9x + 20 = (x + 4)(x + 5), so x = -4 or -5. y² + 5y + 6 = (y + 2)(y + 3), so y = -2 or -3; both possible x-values are less than both…
Correct answer: If x < y11. I. x2 - x - 42 = 0, II. y2 - 17y + 72 = 0 to solve both the equations to find the values of x and y?
- A. If x < y
- B. If x > y
- C. If x ≤ y
- D. If x ≥ y
- E. If x = y or the relationship between x and y cannot be established.
Explanation: Factoring the first equation gives (x - 7)(x + 6) = 0, so x = 7 or -6. The second gives (y - 8)(y - 9) = 0, so y = 8 or 9; even the larger…
Correct answer: If x < y12. I. x2 + 5x + 6 = 0, II. y2 + 9y +14 = 0 to solve both the equations to find the values of x and y?
- A. If x < y
- B. If x > y
- C. If x ≤ y
- D. If x = y or the relationship between x and y cannot be established.
Explanation: The roots are x = -2 or -3 because x² + 5x + 6 = (x + 2)(x + 3), while y = -7 or -2 because y² + 9y + 14 = (y + 7)(y + 2).
Correct answer: If x = y or the relationship between x and y cannot be established.13. I. a2 + 8a + 16 = 0, II. b2 - 4b + 3 = 0 to solve both the equations to find the values of a and b?
- A. If a < b
- B. If a ≤ b
- C. If the relationship between a and b cannot be established
- D. If a > b
Explanation: a² + 8a + 16 = (a + 4)², so a = -4. Also, b² - 4b + 3 = (b - 1)(b - 3), so b = 1 or 3; therefore a is less than either possible value of…
Correct answer: If a < b- A. If a < b
- B. If a ≤ b
- C. If the relationship between a and b cannot be established
- D. If a > b
Explanation: a² + 11a + 30 = (a + 5)(a + 6), giving a = -5 or -6. b² + 6b + 5 = (b + 1)(b + 5), giving b = -1 or -5; every a-value is less than or…
Correct answer: If a ≤ b- A. If a < b
- B. If a ≤ b
- C. If the relationship between a and b cannot be established
- D. If a ≥ b
Explanation: a² - 9a + 20 = (a - 4)(a - 5), so a = 4 or 5. For b, 2b² - 5b - 12 = (2b + 3)(b - 4), so b = -3/2 or 4; hence every possible a is greater…
Correct answer: If a ≥ b- A. if a < b
- B. if a ≤ b
- C. if the relationship between a and b cannot be established.
- D. if a > b
Explanation: a² - 7a + 12 = (a - 3)(a - 4), so a = 3 or 4. b² - 3b + 2 = (b - 1)(b - 2), so b = 1 or 2; therefore every possible a-value is greater…
Correct answer: if a > b- A. 10
- B. 8
- C. 15
- D. 7.50
Explanation: Let the price of one notebook be p rupees, so the number bought is 300/p.
Correct answer: 10- A. 3x2 + 5x - 2 = 0
- B. 3x2 + 5x + 2 = 0
- C. 3x2 - 5x + 2 = 0
- D. 3x2 - 5x - 2 = 0
Explanation: If r is a root of 2r² + 5r + 3 = 0 and z = 1/r, substitute r = 1/z: 2/z² + 5/z + 3 = 0.
Correct answer: 3x2 + 5x + 2 = 019. Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 8x + 4 = 0?
- A. 15
- B. 14
- C. 24
- D. 26
Explanation: For x² + 8x + 4 = 0, Vieta's relations give a + b = -8 and ab = 4. Therefore a/b + b/a = (a² + b²)/ab = ((a + b)² - 2ab)/ab = (64 - 8)/4 =…
Correct answer: 14- A. -21
- B. 1
- C. 61
- D. 21
Explanation: For x² - 9x + 20 = 0, the sum of roots is a + b = 9 and their product is ab = 20.
Correct answer: 61Quadratic Equations MCQs: common questions
Are these Quadratic Equations MCQs free?
Yes. All Quadratic Equations MCQs from Mathematics are free on TestUstad, with unlimited attempts and no account needed. Nothing on this page is a sample or a trial.
How many Quadratic Equations MCQs are on this page?
There are 28 Quadratic Equations MCQs in the Mathematics bank, shown 20 to a page with the correct answer and an explanation on each.
Does every Quadratic Equations MCQ have an explanation?
Yes. Each Quadratic Equations question shows the correct option and a written explanation of why it is correct, so a wrong answer teaches you something rather than just being marked wrong.
Can I take a timed Quadratic Equations test?
Yes. The practice button on this page starts a free Quadratic Equations test drawn from the Mathematics bank. It marks each answer instantly, gives you a score at the end, and can be retaken as many times as you like.