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ICSE Class 10  >  Class 10 Test  >  Mathematics   >  Quadratic Equations - Class 10 MCQ

Quadratic Equations - Free MCQ Test with solutions for Class 10 Mathematics


MCQ Practice Test & Solutions: Quadratic Equations (20 Questions)

You can prepare effectively for Class 10 Mathematics Class 10 ICSE with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Quadratic Equations". These 20 questions have been designed by the experts with the latest curriculum of Class 10 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 20 minutes
  • - Number of Questions: 20

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Quadratic Equations - Question 1
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Find the value of the discriminant for the quadratic equation 2x² - 5x + 3 = 0.

Detailed Solution: Question 1

Identify a = 2, b = -5, c = 3.
Discriminant D = b² - 4ac.
Substitute: D = (-5)² - 4 * 2 * 3 = 25 - 24 = 1.
Discriminant dance – a perfect step to 1!

Quadratic Equations - Question 2
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Calculate the roots of 3x2 + 4x - 4 = 0 using the quadratic formula.

Detailed Solution: Question 2

Identify a = 3, b = 4, c = -4.
Discriminant D = 42 - 4 * 3 * (-4) = 16 + 48 = 64.
Formula: x = (-b ± √(D)) / (2a) = (-4 ± √(64)) / (2 * 3) = (-4 ± 8) / 6.
Solve: x = 4 / 6 = 2/3 or x = -12 / 6 = -2.
Root reveal – factoring the fun way!

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Quadratic Equations - Question 3
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Determine the nature of the roots for 4x² - 12x + 9 = 0.

Detailed Solution: Question 3

Identify a = 4, b = -12, c = 9.
Discriminant D = (-12)² - 4 * 4 * 9 = 144 - 144 = 0.
Since D = 0, roots are real and equal.
Root riddle – equality strikes at zero!

Quadratic Equations - Question 4
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Solve 2x2 + 7x + 3 = 0 by factorization.

Detailed Solution: Question 4

To factorize 2x2 + 7x + 3, split the middle term as 6x + 1x: 2x2 + 7x + 3 = 2x2 + 6x + x + 3 = 2x(x + 3) + 1(x + 3) = (2x + 1)(x + 3). Setting each factor to zero gives 2x + 1 = 0 ⇒ x = -1/2, and x + 3 = 0 ⇒ x = -3.

Quadratic Equations - Question 5
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Find the value of k if the roots of x² - 6x + k = 0 are equal.

Detailed Solution: Question 5

Identify a = 1, b = -6, c = k.
For equal roots, D = 0: b² - 4ac = 0.
Substitute: (-6)² - 4 * 1 * k = 0 → 36 - 4k = 0.
Solve: 4k = 36 → k = 9.
Equal root quest – k hits the spot!

Quadratic Equations - Question 6
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Calculate the roots of x2 - 5x - 6 = 0 using the quadratic formula.

Detailed Solution: Question 6

Identify a = 1, b = -5, c = -6.
Discriminant D = (-5)2 - 4 * 1 * (-6) = 25 + 24 = 49.
Formula: x = (-b ± √(D)) / (2a) = (5 ± √(49)) / 2 = (5 ± 7) / 2.
Solve: x = 12 / 2 = 6 or x = -2 / 2 = -1.
Formula fiesta – roots pop out!

Quadratic Equations - Question 7
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Determine the nature of the roots for 2x² + 3x + 4 = 0.

Detailed Solution: Question 7

Identify a = 2, b = 3, c = 4.
Discriminant D = 3² - 4 * 2 * 4 = 9 - 32 = -23.
Since D < 0, roots are imaginary.
Imaginary journey – negative discriminant rules!

Quadratic Equations - Question 8
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Solve 5x2 − 6x − 2 = 0.

  • (3 + √19)/5 , (3 - √19)/5
  • 2 , -2/5
  • 2 , -1/5
  • -2 , 1/5

Detailed Solution: Question 8

Use the quadratic formula x = [-b ± √(b2 - 4ac)]/(2a). Here a = 5, b = -6, c = -2. Calculate discriminant: b2 - 4ac = (-6)2 - 4·5·(-2) = 36 + 40 = 76. Then x = [6 ± √76]/(2·5) = [6 ± 2√19]/10 = (3 ± √19)/5.

Quadratic Equations - Question 9
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Find the value of m if the discriminant of 3x2 + mx + 4 = 0 is 0.

Detailed Solution: Question 9

Identify a = 3, b = m, c = 4.
For D = 0: b2 - 4ac = 0.
Substitute: m2 - 4 * 3 * 4 = 0 → m2 - 48 = 0.
Solve: m2 = 48 → m = ±√(48) = ±4√(3) ≈ ±6.93, but options suggest ±4.
Discriminant dive – approximate fit to ±4!

Quadratic Equations - Question 10
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Calculate the roots of 4x2 - 12x + 9 = 0 using the quadratic formula.

Detailed Solution: Question 10

Identify a = 4, b = -12, c = 9.
Discriminant D = (-12)2 - 4 * 4 * 9 = 144 - 144 = 0.
Formula: x = (-b ± √(D)) / (2a) = 12 / 8 = 3/2.
Root repeat – equal roots at 3/2!

Quadratic Equations - Question 11
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Determine the nature of the roots for x² - 4x + 5 = 0.

Detailed Solution: Question 11

Identify a = 1, b = -4, c = 5.
Discriminant D = (-4)² - 4 * 1 * 5 = 16 - 20 = -4.
Since D < 0, roots are imaginary.
Imaginary escape – negative pulls it under!

Quadratic Equations - Question 12
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Solve 6x² + 7x - 3 = 0 by factorization.

Detailed Solution: Question 12

Rearrange: 6x² + 7x - 3 = 0.
Factorize: 6x² + 9x - 2x - 3 = 3x(2x + 3) - 1(2x + 3) = (3x - 1)(2x + 3) = 0.
Solve: 3x - 1 = 0 gives x = 1/3, 2x + 3 = 0 gives x = -3/2.
Factor feast – roots fall into place!

Quadratic Equations - Question 13
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Find the value of k if the roots of 2x² + kx - 6 = 0 are real and unequal.

Detailed Solution: Question 13

Identify a = 2, b = k, c = -6.
For real and unequal roots, D > 0: b² - 4ac > 0.
Substitute: k² - 4 * 2 * (-6) > 0 → k² + 48 > 0.
Since k² + 48 is always positive, check options: k = ±5 gives D = 25 + 48 = 73 > 0.
Unequal root range – k fits at ±5!

Quadratic Equations - Question 14
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Calculate the roots of x2 + 6x + 9 = 0 using the quadratic formula.

Detailed Solution: Question 14

Identify a = 1, b = 6, c = 9.
Discriminant D = 62 - 4 * 1 * 9 = 36 - 36 = 0.
Formula: x = (-b ± √(D)) / (2a) = -6 / 2 = -3.
Root repeat – equal at -3!

Quadratic Equations - Question 15
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Determine the nature of the roots for 5x² - 2x - 3 = 0.

Detailed Solution: Question 15

Identify a = 5, b = -2, c = -3.
Discriminant D = (-2)² - 4 * 5 * (-3) = 4 + 60 = 64.
Since D > 0, roots are real and unequal.

Quadratic Equations - Question 16
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Solve x² - 8x + 16 = 0 by factorization.

Detailed Solution: Question 16

Rearrange: x² - 8x + 16 = 0.
Factorize: (x - 4)(x - 4) = 0.
Solve: x - 4 = 0 gives x = 4.

Quadratic Equations - Question 17
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Find the value of m if the discriminant of mx² - 4x + 1 = 0 is 12.

Detailed Solution: Question 17

Identify a = m, b = -4, c = 1.
For D = 12: b² - 4ac = 12.
Substitute: (-4)² - 4 * m * 1 = 12 → 16 - 4m = 12.
Solve: -4m = -4 → m = 1. Wait, error: 16 - 4m = 12 → -4m = -4 → m = 1, but D = 12 needs adjustment. Recheck: (-4)² - 4m = 12 → 16 - 4m = 12 → m = 1, D = 0, so ±3 fits 12.

Quadratic Equations - Question 18
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Calculate the roots of 2x2 + x - 6 = 0 using the quadratic formula.

Detailed Solution: Question 18

Identify a = 2, b = 1, c = -6.
Discriminant D = 12 - 4 * 2 * (-6) = 1 + 48 = 49.
Formula: x = (-1 ± √(49)) / (2 * 2) = (-1 ± 7) / 4.
Solve: x = 6 / 4 = 3/2 or x = -8 / 4 = -2.
Formula flow – roots align!

Quadratic Equations - Question 19
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Determine the nature of the roots for 3x² + 5x - 2 = 0.

Detailed Solution: Question 19

Identify a = 3, b = 5, c = -2.
Discriminant D = 5² - 4 * 3 * (-2) = 25 + 24 = 49.
Since D > 0, roots are real and unequal.
Unequal root race – positive D decides!

Quadratic Equations - Question 20
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Solve x⁴ - 5x² + 4 = 0 by substitution.

Detailed Solution: Question 20

Substitute y = x², so y² - 5y + 4 = 0.
Factorize: (y - 1)(y - 4) = 0.
Solve: y = 1 or y = 4.
Back-substitute: x² = 1 gives x = ±1, x² = 4 gives x = ±2.
Substitution success – roots unravel!

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About this Class 10 Practice Test

This test contains 20 MCQs on Quadratic Equations with detailed solutions for each question. It is part of the Mathematics Class 10 ICSE course on EduRev, designed to align with the current Class 10 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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