Important CBSE MCQs Class 10th Maths from Chapter 4 Quadratic Equations with Solutions 2023-24

Physics Wallah Academic Expert
December 07, 2023

CBSE MCQs Class 10th Maths: Board Exam of CBSE Class 10 Maths, students can expect Multiple Choice Type Questions. Achieving a high score on these questions necessitates a thorough review of the fundamental concepts. To facilitate students' exam preparations, we have compiled MCQs based on crucial ideas and topics from Class 10 Maths.

In this article, we present a set of MCQs about Math Chapter 4: Quadratic Equations. Answers and comprehensive explanations accompany each of these questions. By exploring the MCQs below, you can gain insight into the CBSE MCQs Class 10th Maths likely to appear on the CBSE Class 10 Maths Exam for the academic year 2023-2024.

CBSE MCQs Class 10th Maths Overview

The CBSE MCQs Class 10th Maths typically introduces a set of multiple-choice questions (MCQs) for the 10th-grade mathematics curriculum as per the Central Board of Secondary Education (CBSE) guidelines. These MCQs are designed to assess students' understanding of key mathematical concepts, providing a quick and effective way for self-assessment and exam preparation. 

It often includes information on the number of questions and the distribution of marks or weightage. It may highlight the importance of practicing MCQs as preparation for the CBSE Class 10 Mathematics examination.

Also Read: CBSE Board Exams 2024

Online multiple-choice questions for all Class 10 Maths chapters are available here to assist students in their exam preparations. These objective questions comprehensively cover the concepts explained in each chapter, allowing students to gauge their exam readiness.

Using these resources, students can enhance their performance in upcoming board exams and excel in competitive assessments, including Math Olympiads. We recommend students use problem-solving skills to tackle these MCQs and verify their answers. Additionally, try to adhere to a time limit for each question.

Here is the list of chapters with links to the corresponding multiple-choice questions. Click on the respective link to download the answers and supplementary PDFs for additional practice.

CBSE Class 10th 2024 Overview

Board Name Central Board of Secondary Education, Delhi
Examination Name CBSE Board Exam 2024
Class Name 10th and 12th Class
Category Time Table
Session 2023-24
Exam Dates for Class 10th 15 February to 10th April 2024
Exam Type Theory and Practical Exam
Official Website www.cbse.gov.in

Also Read: ICSE Class 10 Date Sheet 2024

Class 10 Quadratic Equations Important Questions

Here are class 10th quadratic equation questions that are important, and you must practice them:

1) Solve the quadratic equation: 2x^2 - 7x + 3 = 0 using the quadratic formula.

Solution: Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a

For the given equation: a = 2, b = -7, c = 3

Calculate the discriminant: D = b^2 - 4ac = (-7)^2 - 4 * 2 * 3 = 49 - 24 = 25

Since D > 0, the equation has two distinct real roots.

Now, apply the quadratic formula:

x = (-(-7) ± √25) / (2 * 2) = (7 ± 5) / 4

So, the roots are: x₁ = (7 + 5)/4 = 3 and x₂ = (7 - 5)/4 = ½

 

2) Determine the discriminant of the quadratic equation: 5x^2 - 2x - 3 = 0 and state the nature of its roots.

Solution: For the given equation: a = 5, b = -2, c = -3

Calculate the discriminant: D = b^2 - 4ac = (-2)^2 - 4 * 5 * (-3) = 4 + 60 = 64

Since D > 0, the equation has two distinct real roots.

3) If one root of a quadratic equation is 4, and the equation is monic, find the other root.

Solution: If one root is 4, then by Vieta's formulas, the sum of the roots is equal to -b/a. So, the sum of the roots is 4 + r, where r is the other root. According to Vieta's formulas, this sum equals -b/a.

Therefore, -b/a = 4 + r, which implies r = -b/a - 4.

 

4) Solve the equation: 3x^2 + 10x = 8 by completing the square.

Solution: First, move 8 to the left side to make it 3x^2 + 10x - 8 = 0.

Now, complete the square by adding and subtracting (10/2)^2 = 25 to the equation:

3x^2 + 10x + 25 - 25 - 8 = 0

This can be factored into a perfect square: (3x + 5)^2 - 33 = 0

Solve for x: (3x + 5)^2 = 33

Taking the square root of both sides: 3x + 5 = ±√33

Now, isolate x: 3x = -5 ± √33

Finally: x = (-5 ± √33)/3

 

5) Find the roots of the quadratic equation: x^2 - 6x + 9 = 0 by factoring.

Solution: The given equation is a perfect square trinomial: (x - 3)^2 = 0

Take the square root of both sides: x - 3 = 0

Solve for x: x = 3

So, the equation has a repeated real root at x = 3.

 

6) If the roots of a quadratic equation are -2 and 7, write down the equation in the standard form.

Solution: If the roots of the quadratic equation are -2 and 7, then the equation can be written as follows:

(x - (-2))(x - 7) = (x + 2)(x - 7) = 0

Expanding this equation:

x^2 - 7x + 2x - 14 = x^2 - 5x - 14

So, the equation in standard form is x^2 - 5x - 14 = 0.

 

7) Determine the value of k for which the equation 2x^2 - kx + 8 = 0 has equal roots.

Solution: For the roots to be equal, the discriminant D = 0.

For the given equation: a = 2, b = -k, c = 8

Set D = 0: (-k)^2 - 4 * 2 * 8 = 0

Solve for k: k^2 - 64 = 0

k^2 = 64

k = ±√64

k = ±8

 

8) Given the quadratic equation x^2 - 4x + k = 0, find the value of k so that the roots are real and unequal.

Solution: For real and unequal roots, the discriminant D > 0.

For the given equation: a = 1, b = -4, c = k

Set D > 0: (-4)^2 - 4 * 1 * k > 0

Solve for k: 16 - 4k > 0

-4k > -16

k < 4

So, for real and unequal roots, k should be less than 4.

 

9) If the roots of the equation 3x^2 - 2kx + 2k = 0 are equal, find the value of k.

Solution: For equal roots, the discriminant D = 0.

For the given equation: a = 3, b = -2k, c = 2k

Set D = 0: (-2k)^2 - 4 * 3 * 2k = 0

Solve for k: 4k^2 - 24k = 0

4k(k - 6) = 0

k(k - 6) = 0

k = 0 or k = 6

So, for equal roots, k can be 0 or 6.

 

10) Find the roots of the quadratic equation x^2 + 5x + 6 = 0 using the factorization method.

Solution: To factor the quadratic equation, find two numbers that multiply by 6 and add up to 5. These numbers are 2 and 3.

So, the equation can be factored as (x + 2)(x + 3) = 0.

Set each factor to zero: x + 2 = 0 and x + 3 = 0.

Solve for x: x = -2 and x = -3.

The roots of the equation are x = -2 and x = -3.

Using books for practicing MCQs is also the best way for 10th class preparation. CBSE Class 10th - Past 10 Years' Solved Papers (2023-2014) by PW is the ideal book for CBSE MCQs Class 10th Maths.

Also Read: CBSE Sample Paper Class 10

Class 10 Quadratic Equations Extra Questions

Here are some other class 10 quadratic equations important extra questions:

1) Solve for x in the equation 2x^2 - 3x - 5 = 0:

Solution: Using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For this equation (a = 2, b = -3, c = -5):

x = (3 ± √((-3)² - 4 * 2 * (-5))) / (2 * 2)

x = (3 ± √(9 + 40)) / 4

x = (3 ± √49) / 4

x = (3 ± 7) / 4

So, the solutions are:

x₁ = (3 + 7) / 4 = 10 / 4 = 2.5

x₂ = (3 - 7) / 4 = -4 / 4 = -1

 

2) Find the value of k for which the equation kx^2 - 4x + 3 = 0 has real and equal roots:

Solution: For real and equal roots, the discriminant (D) should be equal to 0.

D = b² - 4ac = (-4)² - 4 * k * 3 = 16 - 12k

Setting D = 0:

16 - 12k = 0

12k = 16

k = 16 / 12

k = 4 / 3

 

3) Simplify and solve the equation: (x - 1)(x - 2) = 0:

Solution: To solve this equation, set each factor equal to zero:

x - 1 = 0

x = 1

x - 2 = 0

x = 2

The solutions are x = 1 and x = 2.

 

4) Determine the values of m for which the equation mx^2 - 3x + 2m = 0 has two distinct real roots:

Solution: For two distinct real roots, the discriminant (D) should be greater than 0.

D = b² - 4ac = (-3)² - 4 * m * 2m = 9 - 8m²

For D > 0:

9 - 8m² > 0

8m² < 9

m² < 9/8

m < √(9/8)

So, the values of m are in the range (-√(9/8), √(9/8)).

 

5) Solve for x in the equation x^2 - 7x + 10 = 0 using the method of factorization:

Solution: To factor this equation, find two numbers whose sum is -7 and whose product is 10.

These numbers are -5 and -2.

So, the equation can be factored as:

(x - 5)(x - 2) = 0

Setting each factor equal to zero:

x - 5 = 0

x = 5

x - 2 = 0

x = 2

The solutions are x = 5 and x = 2.

 

6) For what values of p, the equation px^2 + 3x - 2 = 0 has real roots:

Solution: For real roots, the discriminant (D) should be greater than or equal to 0.

D = b² - 4ac = (3)² - 4 * p * (-2) = 9 + 8p

For D ≥ 0:

9 + 8p ≥ 0

8p ≥ -9

p ≥ -9/8

So, the values of p are greater than or equal to -9/8.

 

7) If one root of the equation x^2 - px + 9 = 0 is 3, find the other root:

Solution: If one root is 3, then the product of the roots is equal to the constant term (9).

Let the other root be α:

(3)α = 9

α = 9/3

α = 3

So, the other root is also 3.

 

8) Determine the value of k for which the equation x^2 + kx + 9 = 0 has no real roots:

Solution: For no real roots, the discriminant (D) should be less than 0.

D = b² - 4ac = (k)² - 4 * 1 * 9 = k² - 36

For D < 0:

k² - 36 < 0

k² < 36

k < ±√36

k < ±6

The values of k are between -6 and 6.

 

9) Simplify and solve the equation: (2x + 3)(3x - 5) = 0:

Solution: To solve this equation, set each factor equal to zero:

2x + 3 = 0

2x = -3

x = -3/2

3x - 5 = 0

3x = 5

x = 5/3

The solutions are x = -3/2 and x = 5/3.

 

10) If the roots of the equation x^2 - mx + 16 = 0 are equal, find the value of m:

Solution: For equal roots, the discriminant (D) should be equal to 0.

D = b² - 4ac = (-m)² - 4 * 1 * 16 = m² - 64

Setting D = 0:

m² - 64 = 0

m² = 64

m = ±√64

m = ±8

So, the value of m is either 8 or -8.

The CBSE 15 Sample Question Papers Class 10 Mathematics (Standard) for 2024 Exam by PW is a comprehensive book designed to help students prepare for their Class 10 Mathematics board exam. The book starts with cheat sheets and quick reference guides summarizing essential concepts and formulas. These are helpful for last-minute revisions. The book offers a comparative analysis between CBSE SQPs and the 2023 paper, providing insights into the trends and question patterns that can be expected in the upcoming exam.

Class 10 Quadratic Equations Extra Questions With Solutions

Here are some of the Class 10 Quadratic Equations Important Questions With Solutions:

1. Equation of (x+1)2-x2=0 has several real roots equal to:

(a) 1

(b) 2

(c) 3

(d) 4

Answer: (a) 1

 

2. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, the other two sides of the triangle are equal to:

(a) Base=10cm and Altitude=5cm

(b) Base=12cm and Altitude=5cm

(c) Base=14cm and Altitude=10cm

(d) Base=12cm and Altitude=10cm

Answer: (b) Base=12cm and Altitude=5cm

 

3. The sum of two numbers is 27, and the product is 182. The numbers are:

(a) 12 and 13

(b) 13 and 14

(c) 12 and 15

(d) 13 and 24

Answer: (b) 13 and 14

 

4. If ½ is a root of the quadratic equation x2-mx-5/4=0, then value of m is:

(a) 2

(b) -2

(c) -3

(d) 3

Answer: (b) -2

 

5. If one root of equation 4x2-2x+k-4=0 is reciprocal of the other. The value of k is:

(a) -8

(b) 8

(c) -4

(d) 4

Answer: (b) 8

 

6. The roots of 100x2 – 20x + 1 = 0 is:

(a) 1/20 and 1/20

(b) 1/10 and 1/20

(c) 1/10 and 1/10

(d) None of the above

Answer: (c) 1/10 and 1/10

 

7. The value of 6+6+6……… is: 

(a) 4

(b) 3

(c) 3.5

(d) -3

Answer: (b) 3

 

8. The sum of the reciprocals of Rehman's ages 3 years ago and 5 years from now is 1/3. The present age of Rehman is:

(a) 7

(b) 10

(c) 5

(d) 6

Answer: (a) 7

 

9. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

A. 30 km/hr

B. 40 km/hr

C. 50 km/hr

D. 60 km/hr

Answer: (b) 40 km/hr

 

10. The roots of quadratic equation 2x2 + x + 4 = 0 are:

(a) Positive and negative

(b) Both Positive

(c) Both Negative

(d) No real roots

Answer: (d) No real roots

CBSE 15 Sample Question Papers Class 10 Mathematics (Standard) for 2024 exam | PYQ 2023 Paper with Topper's Explanations by PW is a well-structured and feature-rich resource to aid Class 10 students in their mathematics exam preparation. It not only offers ample practice material but also valuable insights and guidance to excel in the board exams.

10 Quadratic Equations Examples

Basic Quadratic Equation:

  • Example: x^2 - 4x + 4 = 0

  • This is a simple quadratic equation that can be factored as (x - 2)(x - 2) = 0, giving one real root x = 2 with multiplicity 2.

Quadratic Equation with Real Roots:

  • Example: x^2 - 5x + 6 = 0

  • Factoring it, we get (x - 2)(x - 3) = 0, yielding two real roots, x = 2 and x = 3.

Quadratic Equation with Complex Roots:

  • Example: x^2 + 4x + 5 = 0

  • Solving using the quadratic formula, we get complex roots: x = -2 + i and x = -2 - i.

Quadratic Equation with Rational Roots:

  • Example: 2x^2 - 7x + 3 = 0

  • Factoring it, we find (2x - 1)(x - 3) = 0. The roots are x = 1/2 and x = 3.

Quadratic Equation with Negative Discriminant (No Real Roots):

  • Example: x^2 + 2x + 5 = 0

  • The discriminant (b² - 4ac) is negative, indicating no real roots. Using the quadratic formula, we get complex roots.

Quadratic Equation with One Real and One Complex Root:

  • Example: x^2 - 4x + 8 = 0

  • Solving it, we find one real root x = 2 and one complex root x = 2 + 2i.

Quadratic Equation with Fractional Coefficients:

  • Example: 1/2x^2 - 3/4x + 1/8 = 0

  • Multiply through by 8 to clear fractions and solve.

Quadratic Equation with Higher Order Terms:

  • Example: 3x^4 - 7x^2 + 2 = 0

  • This is a quartic equation, but it can be reduced to a quadratic equation by substitution (e.g., by letting y = x²).

Quadratic Equation with Word Problem:

  • Example: The product of two consecutive positive integers is 132. What are the integers?

  • This can be translated into the quadratic equation x(x + 1) = 132.

Quadratic Equation with Inequalities:

  • Example: x^2 - 3x - 4 < 0

  • Solve for x, and you'll find the range of values for which this quadratic expression is less than 0.

If you want a detailed explanation of all previous year's MCQs, you must find the best books and quality study materials. Check the PW store to buy high-quality study materials and books for your Class 10th exam preparation!

What are the Chapters in Class 10 Maths?

You must be wondering how many chapters there are in class 10th maths. There are 15 chapters in Class 10 Maths that are listed below in the table:

Chapters in Class 10 Maths:

Chapter Number Chapter Name
1 Real Numbers
2 Polynomials
3 Pair of Linear Equations in Two Variables
4 Quadratic Equations
5 Arithmetic Progressions
6 Triangles
7 Coordinate Geometry
8 Introduction to Trigonometry
9 Some Applications of Trigonometry
10 Circles
11 Constructions
12 Areas Related to Circles
13 Surface Areas and Volumes
14 Statistics
15 Probability

CBSE MCQs Class 10th Maths FAQ's

1. What are CBSE MCQs Class 10th Maths?

Ans: CBSE MCQs Class 10th Maths are multiple-choice questions designed to test your understanding of various mathematical concepts and topics. They are part of the examination pattern and can help you score well on board exams.

2. Are these MCQs important for the Class 10th Maths board exam?

Ans: Yes, MCQs are an integral part of the Class 10th Maths board exam. Scoring well on these questions can significantly boost your overall score.

3. How can I access CBSE MCQs Class 10th Maths?

Ans: You can access CBSE MCQs Class 10th Maths online through various educational websites like PW and online platforms. They are also available in your NCERT textbook.

4. Are answers provided for these MCQs?

Ans: Yes, answers are typically provided along with the CBSE MCQs Class 10th Maths to help you verify your responses and understand the correct solutions.

5. How should I prepare for Class 10th Maths MCQs?

Ans: To prepare for CBSE MCQs Class 10th Maths, it's essential to understand the concepts and practice solving similar questions thoroughly. Time management is crucial, so practice solving MCQs within a stipulated time frame.

6. Can I use CBSE Class 10th Maths MCQs for competitive exam preparation?

Ans: Yes, practicing CBSE MCQs Class 10th Maths can be helpful for competitive exams that include MCQ sections, as it enhances your problem-solving skills and conceptual understanding.

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