MCQs on Chapter 4: Quadratic Equations for Class 10 Maths

Quadratic Equations Class 10 MCQs are available in this Maths article. These Multiple Choice Questions are very useful in revising the chapter 4 of CBSE Class 10 Maths syllabus in an easy and exam-oriented way. The MCQs with answers and detailed solutions are based on the standard form of quadratic equations , solving quadratic equations , nature of roots , factorisation and relationship between roots and coefficients. This article is helpful in strengthening conceptual understanding, improving problem solving skills and preparing well for board exams.

MCQS on Chapter 4: Quadratic Equations for Class 10 With Answers

Question 1: Which of the following is a quadratic equation?

(a) x³ + 2x + 1 = 0

(b) x² + 1/x² = 2   (x ≠ 0)

(c) 2x² − 3x + 5 = 0

(d) x(x + 1)(x + 2) = 0

Answer: (c) is the correct answer. 

Explanation: It is in the standard form ax² + bx + c = 0 with a = 2, b = −3, c = 5, and a ≠ 0.

Question 2: The equation (x + 1)² = x² − 5 has how many real roots?

(a) One real root

(b) Two distinct real roots

(c) No real roots

(d) Two equal roots

Answer: (a) One real root

Explanation: Expand the left side: x² + 2x + 1 = x² − 5

The x² terms cancels  2x + 1 = −5 ⇒ 2x = −6 ⇒ x = −3. The equation reduces to a linear equation, therefore, exactly one root.

Question 3: If x = −2 is a root of x² + kx − 4 = 0, find the value of k.

(a) k = 0

(b) k = −2

(c) k = 4

(d) k = −4

Answer: (a) k = 0

Explanation: Substitute x = −2: (−2)² + k(−2) − 4 = 0

4 − 2k − 4 = 0 ⇒ −2k = 0 ⇒ k = 0 

Question 4: The roots of 100x² − 20x + 1 = 0 are:

(a) 1/20 and 1/20

(b) 1/10 and 1/20

(c) 1/10 and 1/10

(d) 1/5 and 1/5

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

Explanation: 100x² − 20x + 1 = 0

Split middle term: 100x² − 10x − 10x + 1 = 0

⇒ 10x(10x − 1) − 1(10x − 1) = 0

(10x − 1)² = 0 ⇒ x = 1/10 (repeated root)

Question 5: Solve: 6x² − x − 2 = 0. The roots are:

(a) 2/3 and 1/2

(b) 2/3 and −1/2

(c) −2/3 and 1/2

(d) 1/3 and −1/2

Answer:  (c) −2/3 and 1/2

Explanation: Product a×c = 6×(−2) = −12. Two numbers with product −12 and sum −1: those are −4 and +3.

6x² − 4x + 3x − 2 = 0 ⇒ 2x(3x − 2) + 1(3x − 2) = 0 ⇒ (2x + 1)(3x − 2) = 0

⇒ x = −1/2 or x = 2/3

Question 6: For the equation 2x² − 7x + 3 = 0, the sum of the roots is:

(a) 7

(b) 7/2

(c) 3/2

(d) −7/2

Answer:  (b) 7/2

Explanation: Using the formula, the sum of roots = −b/a = −(−7)/2 = 7/2

Product of roots = c/a = 3/2

Question 7: Using the quadratic formula, the roots of x² − 2x − 2 = 0 are:

(a) 1 ± √2

(b) 1 ± √3

(c) 2 ± √3

(d) −1 ± √3

Answer: (b) 1 ± √3

Explanation: a = 1, b = −2, c = −2

D = b² − 4ac =  (−2)² − 4(1)(−2) = 4 + 8 = 12

√D = √12 = 2√3

x = (-b ± √D)/2a = (2 ± 2√3)/2 = 1 ± √3

Question 8: Which value is added to both sides to complete the square in x² + 6x + 2 = 0?

(a) 3

(b) 7

(c) 9

(d) 6

Answer: (b) 7

Explanation: We first move the constant: x² + 6x = −2

Add (b/2)² = (6/2)² = 9 to both sides: x² + 6x + 9 = 7

The value added to the right side is 7 (since −2 + 9 = 7). 

Question 9: The roots of the equation 2x² + x + 4 = 0 are:

(a) Both positive

(b) Both negative

(c) One positive, one negative

(d) No real roots

Answer: (d) No real roots

Explanation: D = b² − 4ac = (1)² − 4(2)(4) = 1 − 32 = −31

Since D < 0, the equation has no real roots.

Question 10: For what value of k does the equation kx² − 6x + 1 = 0 have equal roots?

(a) k = 6

(b) k = 9

(c) k = 3

(d) k = 12

Answer: (b) k = 9

Explanation: For equal roots: D = 0

b² − 4ac = 0 ⇒ (−6)² − 4(k)(1) = 0 ⇒ 36 − 4k = 0 ⇒ 4k = 36 ⇒ k = 9 

Question 11: The equation x² − 4x + 4 = 0 has roots that are:

(a) Real and unequal

(b) Real and equal

(c) Not real

(d) Irrational

Answer: (b) Real and equal

Explanation: D = (−4)² − 4(1)(4) = 16 − 16 = 0. Roots are real and equal as D = 0.

Question 12: Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. What is Rohan's present age?

(a) 6 years

(b) 8 years

(c) 7 years

(d) 10 years

Answer:  (c) 7 years

Explanation: Let Rohan's present age = x. Mother's present age = x + 26.

3 years from now: (x + 3)(x + 29) = 360

⇒ x² + 32x + 87 = 360 ⇒ x² + 32x − 273 = 0

⇒ (x − 7)(x + 39) = 0 ⇒ x = 7 (rejecting negative age as age cannot be negative)

Rohan's present age = 7 years.

Question 13: The sum of two numbers is 27, and their product is 182. What are the numbers?

(a) 12 and 15

(b) 13 and 14

(c) 10 and 17

(d) 11 and 16

Answer: (b) 13 and 14

Explanation: Let one number = x. Then the other = 27 − x.

Product: x(27 − x) = 182 ⇒ 27x − x² = 182 ⇒ x² − 27x + 182 = 0

Factorising: (x − 13)(x − 14) = 0 ⇒ x = 13 or 14

The numbers are 13 and 14.

Question 14: A rectangular garden has area 800 m². If the length is 20 m more than its width, what is the width of the garden?

(a) 15 m

(b) 25 m

(c) 20 m

(d) 10 m

Answer: (c) 20 m 

Explanation: Let width = w. Length = w + 20. Area = w(w + 20) = 800

w² + 20w − 800 = 0 ⇒ (w + 40)(w − 20) = 0 ⇒ w = 20 (rejecting −40 as length cannot be negative)

Therefore, Width = 20 m and  length = 40 m 

Question 15: For the equation 2x² + kx + 3 = 0 to have real roots, the condition on k is:

(a) k² ≥ 12

(b) k ≥ 2√6

(c) k² ≥ 24

(d) k ≥ √6

Answer: (b) k ≥ 2√6

Explanation: For real roots: D ≥ 0

k² − 4(2)(3) ≥ 0  ⇒ k² − 24 ≥ 0  ⇒  k² ≥ 24

i.e., k ≥ 2√6 or k ≤ −2√6.

 

Click here to download the free PDF of MCQs Worksheet on Chapter 4 Quadratic Equations for Class 10 Maths based on the updated NCERT & CBSE pattern with important multiple-choice questions and answers.

MCQs Worksheet on Chapter 4 Quadratic Equations for Class 10