Students can refer to the following Quadratic Equation MCQ Questions for Class 10 with Answers provided below based on the latest curriculum and examination pattern issued by CBSE and NCERT. Our teachers have provided here a collection of multiple choice questions for Quadratic Equation Class 10 covering all topics in your textbook so that students can assess themselves on all important topics and thoroughly prepare for their exams

**Quadratic Equation MCQ Questions for Class 10 with Answers**

We have provided below chapter wise MCQs questions for Class 10 Mathematics Quadratic Equation with answers which will help the students to go through the entire syllabus and practice multiple choice questions provided here with solutions. As Quadratic Equation MCQs in Class 10 pdf download can be really scoring for students, you should go through all problems provided below so that you are able to get more marks in your exams.

**Quadratic Equation MCQ Questions for Class 10**

**Question. The roots of ax _{2} + bx + c = 0, a ≠ 0 are real and unequal, if b^{2} – 4ac is _______.**

(A) = 0

(B) > 0

(C) < 0,

(D) ≥ 0

**Answer**

B

**Question.** If x = √2 +√2 +√2 + ……….. , then _______.

(A) x = 1

(B) 0 < x < 1

(C) x is infinite

(D) x = 2

## **Answer**

D

**Question.** If 2 is a root of the equation x^{2} + bx + 12 = 0 and the equation x^{2} + bx + q = 0 has equal roots, then q is equal to

(A) 8

(B) –8

(C) 16

(D) –16

## **Answer**

C

**Question.** If one root of the equation a(b – c)x^{2} + b(c – a)x + c(a – b) = 0 is 1, then the other root is ___.

(A) b(c – a) / a(b – c)

(A) a(b – c) / c(a – b)

(A) a(b – c) / c(a – b)

(A) b(c – a) / a(b – c)

## **Answer**

D

**Question.** If the roots of the equation (a – b)x^{2} + (b – c)x + (c – a) = 0 are equal. Then _______.

(A) 2b = a + c

(B) 2a = b + c

(C) 2c = a + b

(D) 1/b = 1/a = 1/c

## **Answer**

B

**Question.** One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x^{2} correctly as –6 and 1 respectively. The correct roots are ____.

(A) 3, –2

(B) –3, 2

(C) –6, –1

(D) 6, –1

## **Answer**

D

**Question.** If √x −1 − √x +1+1=0 , then 4x is equal to ________.

(A) 4 √−1

(B) 0

(C) 5

(D) 1/4×1

## **Answer**

C

**Question.** If one of roots of 2x^{2} + ax + 32 = 0 is twice the other root, then the value of a is ________.

(A) −3 √2

(B) 8 √2

(C) 12 √2

(D) −2 √2

## **Answer**

C

**Question.** For what value of a, the roots of the equation 2x^{2} + 6x + a = 0, satisfy the**condition(α/β)+(β/α) < 2 (where a and b are the roots of equation).**

(A) a < 0

(B) –1 < a < 0

(C) –1 < a < 1

(D) None of these

## **Answer**

D

**Question.** Roots of the quadratic equation x^{2} + x – (a + 1)(a + 2) = 0 are ________.

(A) –(a + 1), (a + 2)

(B) (a + 1), –(a + 2)

(C) (a + 1), (a + 2)

(D) –(a + 1), –(a + 2)

## **Answer**

B

**Question.** The roots of the equation 3x + 5 (x)^{1/2 }= √2 can be found by solving ________.

(A) 9x^{2} + 28x + 25 = 0

(B) 9x^{2} + 30x + 25 = 0

(C) 9x^{2} + 28x – 25 = 0

(D) 16x^{2} + 22x – 30 = 0

## **Answer**

A

**Question.** If the roots of the equation (a^{2} + b^{2}) x^{2} – 2b(a + c)x + (b^{2} + c^{2}) = 0 are equal, then ________.

(A) 2b = a + c

(B) b^{2} = ac

(C) b = 2ac/a+b

(D) b = ac

## **Answer**

B

**Question.** Two numbers whose sum is 12 and the absolute value of whose difference is 4 are the roots of the equation ________.

(A) x^{2} – 12x + 30 = 0

(B) x^{2} – 12x + 32 = 0

(C) 2x^{2} – 6x + 7 = 0

(D) 2x^{2} – 24x + 43 = 0

## **Answer**

B

**Question.** The roots of the equation x^{2}/3 + x1/3 – 2 = 0 are ________.

(A) 1, –8

(B) 1, –2

(C) 2/3, 1/3

(D) –2, –8

## **Answer**

A

**Question.** In the equation

**the roots are equal when m = __.**

(A) 1/2

(B) − 1/2

(C) 0

(D) 1

## **Answer**

B

**Question.** In a bangle shop, if the shopkeeper displays the bangles in the form of a square then he is left with 38 bangles. If he wanted to increase the size of square by one unit each side of the square he found that 25 bangles fall short of in completing the square. The actual number of bangles which he had with him in the shop was ________.

(A) 1690

(B) 999

(C) 538

(D) Can’t be determined

## **Answer**

B

**Question.** A man walks a distance of 48 km in a given time. If he walks 2 km/hr faster, he will perform the journey 4 hrs before. His normal rate of walking, is ________.

(A) 3 km/hr (B) 4 km/hr

(C) – 6 km/hr or 4 km/hr

(D) 5 km/hr

## **Answer**

B

**Question. The ratio of the length and breadth of a rectangular photo frame is 3 : 2. Find its length if its area is 864 cm ^{2} . **(A) 34 cm

(B) 26 cm

(C) 24 cm

(D) 36 cm

**Answer**

D

**Question. Find the value of ‘k’ for which x ^{2} – 4x + k = 0 has coincident roots. **

(A) 4

(B) -4

(C) 0

(D) -2

**Answer**

A

**Question. Which of the following is the quadratic equation one of whose roots is 3-2√3 ? **

(A) x^{2} + 6x -3 = 0

(B) x^{2} – 6x – 3 = 0

(C) x^{2} + 6x +3 = 0

(D) x^{2} – 6x + 3 = 0

**Answer**

B

**Question. If a and Rare the roots of the equation x ^{2} -8x + p = 0 such that α^{2} + β^{2} = 40 , find the value of ‘p’. **

(A) 8

(B) 10

(C) 12

(D) 14

**Answer**

C

**Question. Find two consecutive positive odd numbers, the sum of whose squares is 514. **

(A) 11, 13

(B) 15, 17

(C) 11, 9

(D) 13, 15

**Answer**

B

**Question. Which of the following quadratic polynomials can be factorized into a product of real linear factors? **

(A) 2x^{2} – 5x + 9

(B) 2x^{2} + 4x -5

(C) 3x^{2} + 4x + 6

(D) 5x^{2} – 3x + 2

**Answer**

B

**Question. Find two consecutive integers whose product is 600. **

(A) 30, 20

(B) 50, 12

(C) 15, 40

(D) 24, 25

**Answer**

D

**Question. In the quadratic equation 9x ^{2} + ax – 2 = 0 , find the value of a for which x = 1/3 is its solution. **

(A) -2

(B) 3

(C) -4

(D) 6

**Answer**

B

**Question. What is the ratio of the sum and the product of roots of 7x ^{2} -12x +18 = 0 **

(A) 7:12

(B) 2:3

(C) 3:2

(D) 7:18

**Answer**

B

**Question. Find the product of the roots of the quadratic equation 9m2 + 24 m+16 = 0 . **

(A) 4/3

(B) 9/16

(C) 16/9

(D) 3/4

**Answer**

C

**Question.****In the Maths Olympiad of 2020 at Animal Planet, two representatives from the donkey’s side, while solving a quadratic equation, committed the following mistakes.****(i) One of them made a mistake in the constant term and got the roots as 5 and 9.(ii) Another one committed an error in the coefficient of x and he got the roots as 12 and 4. But in the meantime, they realised that they are wrong and they managed to get it right jointly. Find the quadratic equation.**

(A) x

^{2}+ 4x + 14 = 0

(B) 2x

^{2}+ 7x – 24 = 0

(C) x

^{2}– 14x + 48 = 0

(D) 3x

^{2}– 17x + 52 = 0

## **Answer**

C

**Question.** ₹ 6500 were divided equally among a certain number of persons. If there had been 15 more persons, each would have got ₹ 30 less. Find the original number of persons.

(A) 50

(B) 60

(C) 45

(D) 55

## **Answer**

A

**Question.** Swati can row her boat at a speed of 5 km/hr in still water. If it takes her 1 hour more to row the boat 5.25 km upstream than to return downstream, find the speed of the stream.

(A) 5 km/hr

(B) 2 km/hr

(C) 3 km/hr

(D) 4 km/hr

## **Answer**

B

**Question.** Which of the following equations has two distinct real roots?

(A) 2x^{2} – 3 √2x + 9/4 = 0

(B) x^{2} + x – 5 = 0

(C) x^{2} + 3x + 2 √2 = 0

(D) 5x^{2 }– 3x + 1 = 0

## **Answer**

B

**Question.** Read the statements carefully.**Statement – I :** The quadratic equation ax^{2} + bx + c = 0 has two distinct real roots, if b^{2} – 4ac ≥ 0.**Statement – II :** The quadratic equation 2(a^{2} + b2)x^{2} + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.

(A) Both Statement – I and Statement – II are true.

(B) Statement – I is true but Statement – II is false.

(C) Statement – I is false but Statement – II is true.

(D) Both Statement – I and Statement – II are false.

## **Answer**

C

**Question.** If the roots of the equation x^{2} + 2cx + ab = 0 are real and unequal, then the equation x^{2} – 2(a + b)x + a^{2} + b^{2} + 2c^{2} = 0 has ________ roots.

(A) Real

(B) Equal

(C) No real

(D) Can’t be determined

## **Answer**

C

**Question.** Read the statement carefully and state ‘T’ for true and ‘F’ for false

(ii) A line segment AB of length 2 m is divided at C into two parts such that AC^{2 }= AB·CB. The length of the part CB is 3 + √5 .

(iii) Every quadratic equation can have at most two real roots.

(iv) A real number a is said to be root of the quadratic equation ax^{2} + bx + c = 0, if aα^{2} + bα + c = 0.

** (i) (ii) (iii) (iv)**

(A) F T T T

(B) F T T F

(C) T F F T

(D) F F T T

## **Answer**

D

**Question.** The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2×16/21 , find the fraction.

(A) 3/7

(B) 7/3

(C) 4/3

(D) 3/4

## **Answer**

A

** Question.** Identify the correct statement.

(a) The roots of the quadratic equation 2y

^{2}+ 9y = 0 are 0 and -9/2.

(b) The value of ‘k’ for which 4m

^{2}+ k – 15 = 0 has a root m = 3 is 7.

(c) The quadratic equation 2 (4x -11)

^{2}= 0 has two distinct roots.

(d) 7x

^{2}– 12x – 18 = 0 is not a quadratic equation.

## **Answer**

A

** Question.** Which of the following is a quadratic equation?

## **Answer**

D

** Question.** When are the roots of a quadratic equation real and equal?

(a) When the discriminant is positive.

(b) When the discriminant is zero.

(c) When the discriminant is negative.

(d) When the discriminant is non-negative.

## **Answer**

B

** Question.** Which of the following equations has 2 as a root?

(a) 2x

^{2}– 7x + 6 = 0

(b) x

^{2 }– 4x + 5 = 0

(c) 3x

^{2}– 6x – 2 = 0

(d) x

^{2}+ 3x -12 = 0

## **Answer**

A

** Question.** Which of the following is the quadratic equation one of whose roots is 3 – 2√3 ?

(a) x

^{2}+ 6x – 3 = 0

(b) x

^{2 }– 6x – 3 = 0

(c) x

^{2 }+ 6x + 3 = 0

(d) x

^{2}– 6x + 3 = 0

## **Answer**

B

** Question.** The area of a rectangular cardboard is

**80 cm**

^{2}. If its perimeter is 36 cm, find its**length.**

(a) 40 cm

(b) 10 cm

(c) 20 cm

(d) 8 cm

## **Answer**

B

** Question.** Find the sum of the roots of x

^{2}+ x – 210 = 0

(a) -2

(b) 29

(c) 20

(d) -1

## **Answer**

D

** Question.** A two digit number is 4 times the sum of its

**digits and also 16 more than the product of**

**digits. Find the number.**

(a) 48

(b) 36

(c) 44

(d) 32

## **Answer**

A

** Question.** If the product of the roots of x

^{2}– 3x + k = 10 is – 2, what is the value of’ k’?

(a) -2

(b) 8

(c) 12

(d)-8

## **Answer**

B

** Question.** If the roots of x

^{2}+ 4mx + 4m

^{2}+ m + 1 = 0 are real, which of the following is true?

(a) m = – 1

(b) m ≤ – 1

(c) m ≥ -1

(d) m ≥ 0

## **Answer**

B

**Question.** Find the value of ‘p’ for which m = 1/√3 is a root of the eq/uation pm^{2} + ( √3 – √2)m – 1 = 0

(a) √3

(b) √2

(c) √6

(d) √7

## **Answer**

C

**Question**. What is the value of ‘k’ for which 2x^{2} – kx k has equal roots?

(a) 4 only

(b) 0 only

(c) 8 only

(d) 0, 8

## **Answer**

D

**Question.** The sides of two square plots are (2x – 1)m and (5x + 4)m . The area of the second square plot is 9 times the area of the first square plot. Find the side of the larger plot.

(a) 15m

(b) 13m

(c) 31 m

(d) 39m

## **Answer**

D

**Question.****What is the ratio of the sum and the product of roots of 7x ^{2} – 12x + 18 = 0**

(a) 7:12

(b) 2:3

(c) 3:2

(d) 7:18

## **Answer**

B

**Question.** Find the present age of a boy whose age 12**years from now will be the square of his present age.**

(a) 5 years

(b) 7 years

(c) 4 years

(d) 6 years

## **Answer**

C

**Question.** The perimeter and area of a rectangular park are 80 m and 400 m^{2} . What is its length?

(a) 20m

(b) 15m

(c) 30m

(d) 40m

## **Answer**

A

**Question. Find the common root of the equations x ^{2} – 7x + 10 = 0 and x^{2} – 10x + 16 = 0.**

(a) – 2

(b) 3

(c) 5

(d) 2

## **Answer**

D

**Question.** The quadratic equation ax^{2} + bx + c = 0 has no real root. Which of the following is true?

(a) b^{2} – 4ac < 0

(b) b^{2} – 4ac = 0

(c) b^{2} – 4ac > 0

(d) b^{2} + 4ac < 0

## **Answer**

A

** Question. What is the value of ‘k’ for which the roots of the quadratic equation 3x^{2} + 2kx + 27 = 0 are real and equal? **(a) 9 only

(b) -9 only

(c) 9 or-9

(d) Neither 9 nor-9.

## **Answer**

C

**Question.** If the equation ax – 5x + c = 0 has 10 as the sum of the roots and also as the product of the roots, which of the following is true?

(a) a – c = 5

(b) a = 2,c = 3

(c) a = 5, c =1

(d) a = 3, c = 2

## **Answer**

A

**One Word Questions :**

**Question. Solve the quadratic equation : ax² – 2abx = 0.**

**Answer**

x = 0 or x = 2b

**Question. If one root of the quadratic equation x² mx –16 0 is negetive of other then what is the value of m?**

**Answer**

0

**Question. One root of the quadratic equation 2x² 3x k 0 is 1/2. What is the value of k?**

**Answer**

–2

**Question. Difference of the natural number and its reciprocal is 3/2 . What is the number?**

**Answer**

2

**Question. Find the value of discriminant of the equation √3x² – 2 √2x – 2 √3 =0**

**Answer**

32

**Question. What are the two value of z which satisfy the equation z² + 2z – 8 = 0?**

**Answer**

– 4, 2

**Question. What are the two roots of the equation (x + 4) (x – 5) = 0?**

**Answer**

– 4, 5

**Question. Find the value of discriminant in 25x² – 30x + 9 = 0.**

**Answer**

0

**Question. What are the value of p and q if these are the roots of the equation x² + px + q = 0?**

**Answer**

p = 1, q = –2

**Question. If , are the roots of the equation 3x² 7x 3 0 , then what is the value of .**

**Answer**

– 4/3

**Question. What are the two roots of the equation (x + 5)² – 36 = 0?**

**Answer**

1, –11

**Question. The quadratic equation ax² + bx + c has equal roots. What are the roots?**

**Answer**

– b/a

**Question. The length of a hall is 10m more than its breadth. Find the length and breadth of the hall if its area is 600m².**

**Answer**

30m, 20m

**Question. Find the roots of the equation 3x²+2 5x – √5=0 .**

**Answer**

– √5 , √5/3

**Question. If sum of a whole number and its reciprocal is 17/4 , what is the number?**

**Answer**

4

**Question. For what value of p the equation px² + 4x + 1 = 0 will have equal roots?**

**Answer**

4

**Question. The sum S of n successive odd natural numbers starting from 3 is given by the relation S = n(n + 2). Determine n, if the sum is 168.**

**Answer**

n = 12

**Question. If –4 is a root of the equation x² + px – 4 = 0 and the quadratic equation x² + px + k = 0 has equal roots, find the value of k.**

**Answer**

9/4

**Question. One side of the rectangle exceeds the other side by 3cm. If the area of rectangle is 180sq.cm., find the two sides of the rectangle.**

**Answer**

12cm, 15cm

**Question. What value of x will satisfy the equation x² = (x + 5)(x + 3)?**

**Answer**

-15/8

**Question. Find the solutions of quadratic equation : y²+2 √3y+3= 0 .**

**Answer**

y = – √3, – √3

**Question. Find the roots of the equation y2 + 1/2 , y – 1 = 0 .**

**Answer**

-1 + √7/4 , – 1 – √7/4

**Question. What is the equation whose roots are 2+ √3 and 2 – √3 ?**

**Answer**

x² – 4x + 1 = 0

**Question. The product of Ramu’s age (in years) five years ago and his age (in years) nine years later is 15. Determine Ramu’s present age.**

**Answer**

6 years

**Question. What is the solution set of equation 3x² + 5x – 2 = 0?**

**Answer**

{1/3 , -2}