Class 10 Exam > Class 10 Tests > Quadratic Equations - Class 10 MCQ

Quadratic Equations - Class 10 MCQ

Test Description

20 Questions MCQ Test - Quadratic Equations

Quadratic Equations for Class 10 2025 is part of Class 10 preparation. The Quadratic Equations questions and answers have been prepared according to the Class 10 exam syllabus.The Quadratic Equations MCQs are made for Class 10 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Quadratic Equations below.

Solutions of Quadratic Equations questions in English are available as part of our course for Class 10 & Quadratic Equations solutions in Hindi for Class 10 course. Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free. Attempt Quadratic Equations | 20 questions in 20 minutes | Mock test for Class 10 preparation | Free important questions MCQ to study for Class 10 Exam | Download free PDF with solutions

Quadratic Equations - Question 1

Save

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

A.
1
B.
-1
C.
7
D.
-7

Detailed Solution for Quadratic Equations - 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

Save

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

A.
x = -2/3, 2
B.
x = 2/3, -2
C.
x = 1, -4
D.
x = -1, 4

Detailed Solution for Quadratic Equations - 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!

Clear all your doubts with EduRev

Join for Free

Quadratic Equations - Question 3

Save

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

A.
Real and equal
B.
Real and unequal
C.
Imaginary
D.
Irrational

Detailed Solution for Quadratic Equations - 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

Save

Solve 2x² + 7x + 3 = 0 by factorization.

A.
x = -1, -3/2
B.
x = 1, 3/2
C.
x = -1, 3/2
D.
x = 1, -3/2

Detailed Solution for Quadratic Equations - Question 4

Rearrange: 2x² + 7x + 3 = 0.
Factorize: 2x² + 6x + x + 3 = 2x(x + 3) + 1(x + 3) = (2x + 1)(x + 3) = 0.
Solve: 2x + 1 = 0 gives x = -1/2, x + 3 = 0 gives x = -3.
Factor fun – splitting to solve!

Quadratic Equations - Question 5

Save

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

A.
9
B.
6
C.
3
D.
12

Detailed Solution for Quadratic Equations - 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

Save

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

A.
x = 6, -1
B.
x = -6, 1
C.
x = 5, -1
D.
x = -5, 1

Detailed Solution for Quadratic Equations - 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

Save

Determine the nature of the roots for 2x² + 3x + 4 = 0.

A.
Real and equal
B.
Real and unequal
C.
Imaginary
D.
Irrational

Detailed Solution for Quadratic Equations - 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

Save

Solve 5x² - 6x - 2 = 0 by factorization.

A.
x = 2, -1/5
B.
x = -2, 1/5
C.
x = 1, -2/5
D.
x = -1, 2/5

Detailed Solution for Quadratic Equations - Question 8

Rearrange: 5x² - 6x - 2 = 0.
Factorize: 5x² - 10x + 4x - 2 = 5x(x - 2) + 2(x - 2) = (5x + 2)(x - 2) = 0.
Solve: 5x + 2 = 0 gives x = -2/5, x - 2 = 0 gives x = 2.
Factor magic – splitting the difference!

Quadratic Equations - Question 9

Save

Find the value of m if the discriminant of 3x² + mx + 4 = 0 is 0.

A.
±4
B.
±6
C.
±8
D.
±10

Detailed Solution for Quadratic Equations - 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

Save

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

A.
x = 3/2
B.
x = 3/2, -3/2
C.
x = 1, 9/4
D.
x = -3/2

Detailed Solution for Quadratic Equations - 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

Save

Determine the nature of the roots for x² - 4x + 5 = 0.

A.
Real and equal
B.
Real and unequal
C.
Imaginary
D.
Irrational

Detailed Solution for Quadratic Equations - 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

Save

Solve 6x² + 7x - 3 = 0 by factorization.

A.
x = 1/2, -3
B.
x = -1/2, 3
C.
x = 1/3, -3/2
D.
x = -1/3, 3/2

Detailed Solution for Quadratic Equations - 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

Save

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

A.
k = ±5
B.
k = ±6
C.
k = ±7
D.
k = ±8

Detailed Solution for Quadratic Equations - 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

Save

Calculate the roots of x² + 6x + 9 = 0 using the quadratic formula.

A.
x = -3
B.
x = 3
C.
x = -3, 3
D.
x = 0

Detailed Solution for Quadratic Equations - 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

Save

Determine the nature of the roots for 5x² - 2x - 3 = 0.

A.
Real and equal
B.
Real and unequal
C.
Imaginary
D.
Irrational

Detailed Solution for Quadratic Equations - 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

Save

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

A.
x = 4
B.
x = -4
C.
x = 4, -4
D.
x = 0

Detailed Solution for Quadratic Equations - Question 16

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

Quadratic Equations - Question 17

Save

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

A.
±2
B.
±3
C.
±4
D.
±5

Detailed Solution for Quadratic Equations - 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

Save

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

A.
x = 3/2, -2
B.
x = -3/2, 2
C.
x = 1, -6
D.
x = -1, 6

Detailed Solution for Quadratic Equations - 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

Save

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

A.
Real and equal
B.
Real and unequal
C.
Imaginary
D.
Irrational

Detailed Solution for Quadratic Equations - 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

Save

Solve x⁴ - 5x² + 4 = 0 by substitution.

A.
x = ±1, ±2
B.
x = ±2, ±3
C.
x = ±1, ±3
D.
x = ±2, ±4

Detailed Solution for Quadratic Equations - 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!

Information about Quadratic Equations Page

In this test you can find the Exam questions for Quadratic Equations solved & explained in the simplest way possible. Besides giving Questions and answers for Quadratic Equations, EduRev gives you an ample number of Online tests for practice

Download as PDF

Top Courses for Class 10

Join EduRev with a free account

Notes, Videos, Tests & Analysis—All in One Place

Already have an account? Sign in

By continuing, I agree that i am at least 13 years old and have read and agree to the terms of service and privacy policy.

Attempt this test on App!

Get detailed analysis along with solutions of each question.

Open in App

Not Now

Schools

Medical
Non- Medical
Commerce
Humanities
CBSE Class 10
CBSE Class 9
CBSE Class 8
CBSE Class 7
CBSE Class 6
CBSE Class 5
CBSE Class 4
CBSE Class 3
CBSE Class 2
CBSE Class 1

Competitive Examinations

UPSC
NEET
JEE
CLAT
CAT
GMAT
GATE
Railways
SSC
IIT JAM
Defence
Insurance
Teaching
CA Foundation

Technical Exams

GATE
SSC JE
RRB JE
Civil Engineering
Computer Science Engineering
Electrical Engineering
Electronics Engineering
Biotechnology Engineering
Mechanical Engineering
Chemical Engineering

Important Questions for Quadratic Equations

Find all the important questions for Quadratic Equations at EduRev.Get fully prepared for Quadratic Equations with EduRev's comprehensive question bank and test resources. Our platform offers a diverse range of question papers covering various topics within the Quadratic Equations syllabus. Whether you need to review specific subjects or assess your overall readiness, EduRev has you covered. The questions are designed to challenge you and help you gain confidence in tackling the actual exam. Maximize your chances of success by utilizing EduRev's extensive collection of Quadratic Equations resources.

Quadratic Equations MCQs with Answers

Prepare for the Quadratic Equations within the Class 10 exam with comprehensive MCQs and answers at EduRev. Our platform offers a wide range of practice papers, question papers, and mock tests to familiarize you with the exam pattern and syllabus. Access the best books, study materials, and notes curated by toppers to enhance your preparation. Stay updated with the exam date and receive expert preparation tips and paper analysis. Visit EduRev's official website today and access a wealth of videos and coaching resources to excel in your exam.

Online Tests for Quadratic Equations

Practice with a wide array of question papers that follow the exam pattern and syllabus. Our platform offers a user-friendly interface, allowing you to track your progress and identify areas for improvement. Access detailed solutions and explanations for each test to enhance your understanding of concepts. With EduRev's Online Tests, you can build confidence, boost your performance, and ace Quadratic Equations with ease. Join thousands of successful students who have benefited from our trusted online resources.

Education Revolution