# MCQ Chapter 4 Quadratic Equation Class 10 Mathematics

Please refer to Quadratic Equation MCQ Questions Class 10 Mathematics below. These MCQ questions for Class 10 Mathematics with answers have been designed as per the latest NCERT, CBSE books, and syllabus issued for the current academic year. These objective questions for Quadratic Equation will help you to prepare for the exams and get more marks.

## Quadratic Equation MCQ Questions Class 10 Mathematics

Please see solved MCQ Questions for Quadratic Equation in Class 10 Mathematics. All questions and answers have been prepared by expert faculty of standard 10 based on the latest examination guidelines.

### MCQ Questions Class 10 Mathematics Quadratic Equation

Question. If y = 1 is the common root of ly2 +ly +3=0 and y2 +y + m = 0, then the value of ‘lm ’ is
(a) 3
(b) – 4
(c) 4
(d) – 3

A

Question. Rohan’s mother is 26 years older than him. The product of their ages 3 years from now will be 360, then Rohan’s present age is
(a) 6 years
(b) 7 years
(c) 10 years
(d) 8 years

B

Question. If ‘sin α’ and ‘cos α’ are the roots of the equation ax2 + bx + c = 0, then b2 =
(a) a2 + 2ac
(b) a2 +ac
(c) a2 -ac
(d) a2 -2ac

A

Question. The quadratic equation, sum of whose roots is 3√2 and their product is 5, is
(a) x2 +3√2x -5=0
(b) x2 +3√2x +5=0
(c) x2 – 3√2x +5=0
(d) x2 – 3√2x -5=0

D

Question. If ax2 +bx +c =0 has equal roots, then c is equal to
(a) b2/2a
(b) b2/4a
(c) -b2/4a
(d) -b2/2a

B

Question. Which of the following is a quadratic equation?
(a) x2 −x2=(x-1)2
(b) x2 +2x +1=(4-x)2+3
(c) -2x2=(5-x)(2x-2/5)
(d) (k+1) x2+3/2x -5 =0,where k = – 1

A

Question. (x+1)2 −x2 =0  has
(a) no real roots
(b) 1 real root
(c) 2 real roots
(d) 4 real roots

B

Question. 9x2 + 12x + 4 = 0 have
(a) Real and Distinct roots
(b) No real roots
(c) Distinct roots
(d) Real and Equal roots

D

Question. If the equation (a2 +b2)x2 −2(ac+bd)x +c2+d2=0  has equal roots, then
(b) ab=cd
(d) ab=√cd

A

Question. Find the value of ‘p’ for which m = 1/√3 is a root of the equation pm2 + (√3 – √2)m-1= 0
(a) √3
(b) √2
(c) √6
(d) √7

C

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

C

Question. Which of the following statements is true?
(a) x2 + x + 1 = 0 has no real roots.
(b) x2 – 4x +3 = 0 and x2 – x – 2 = 0 have two common roots.
(c) x2 – 3x – 4 = 0 have real and equal roots.
(d) The roots of ax2 + bx + c = 0,a ≠ 0 are reciprocal to each other if a ≠ c .

A

Question. The length and breadth of a rectangle are (3k + 1) cm and (2k – 1) cm respectively. Find the perimeter of the rectangle if its area is 144cm2 .
(a) 50 cm
(b) 10 cm
(c) 32 cm
(d) 25 cm

A

Question. What is the nature of the roots of the quadratic equation 25x2 – 49 = 0 ?
(a) Real and distinct
(b) Real and equal
(c) Irrational
(d) No real roots

A

Question. Divide 63 into two parts such that their product is 962.
(a) 24, 3C
(b) 28, 35
(c) 26, 37
(d) 27, 36

C

Question. A quadratic equation αx2 +5x +β two roots x = 1/3 and x = -2 . Find the respective values of α and β .
(a) 3, 2
(b) 2, -5
(c)-3, 5
(d) 3, -2

D

Question. If a and P are the roots of the equation x2 + kx +12 = 0 such that α – β =1 , what is the value of ‘k’?
(a) 0
(b) ± 5
(c) ±1
(d) ± 7

D

Question. Which of the following equations has 2 as a root?
(a) 2x2 – 7x + 6 = 0
(b) x2 – 4x + 5 = 0
(c) 3x2 – 6x – 2 = 0
(d) x2 + 3x -12 = 0

A

Question. If the roots of x+ 4mx + 4m2 + m+1= 0 are real, which of the following is true?
(a) m= -1
(b) m ≤ -1
(c) m ≥ -1
(d) m ≥ 0

B

Question. What is the value of ‘k’ for which 2x2 + kx + k has equal roots?
(a) 4 only
(b) 0 only
(c) 8 only
(d) 0, 8

D

Question. Find two consecutive even numbers whose product is double that of the greater number.
(a) 1, 3
(b) 4, 6
(c) 2, 4
(d) 6, 8

C

Question. What are the roots of 17a2 – 20a + 10 = 10a2 + 2a + 7 ?
(a) 1/7 , 3
(b) 3 , -1/7
(c) -1/7 , 3
(d) -3 , – 1/7

A

Question. Identify the quadratic equation from the following.
(a) P + 1/P = 1 , P ≠0
(b) P2 + 1/P = 1 , P ≠ 0
(c) x2 – 1/x = 1, x ≠ 0
(d) x2 + 2√x – 1 = 0

A

Question. For what respective values of ‘m’ and ‘n’ are  x = -2/5 and x = 5/3 the roots of mx2 + nx – 10 = 0 ?
(a) 15,-19
(b) -19, 15
(c) 19,-15
(d) -15, 19

A

Question. Find the roots of the quadratic equation
(a) -1/2 , 1
(b) -1 , 1/2
(c) 1/2 , 1
(d) -1 , -1/2

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

D

Question. Identify the factors of 4x2/5 = 4x – 5 .
(a) 2/5 , 2/5
(b) -5/2 , 5/2
(c) 5/2 , 5/2
(d) -2/5 , 2/5

C

Question. The age of a man is the square of his son’s age. A year ago, the man’s age was eight times the age of his son. What is the present age of the man?
(a) 47 years
(b) 49 years
(c) 36 years
(d) 48 years

B

Question. Which of the following statements is correct?
(a) x =1is a root of 2x2 + 3x + 1= 0 .
(b) x = 2 is not a root of 6x2 + 7x – 5 = 0 .
(c) x = -1is a root of 3x2 – x – 1= 0 .
(d) x = – 2/5 is not a root of 5x2 – 8x – 4 = 0

B

Question. If α and β are the roots of 2x2 -3x -1=0 , then the value of α2 +β2 is
(a) 13/2
(b) 13/4
(c) -13/2
(d) -13/4

B

Question. The ratio of sum and the product of the roots of  7x2 −12x +18=0  is
(a) 2:3
(b) 3:2
(c) 7:18
(d) 7:12

A

Question. The sum S of first n even natural numbers is given by the relation S = n(n +1). If the sum is 420, then the value of ‘n’ is
(a) 20
(b) 21
(c) 24
(d) 22

A

Question. The discriminant of the equation (2a + b) x = x2 + 2ab is ______
(a) (2a + b2)
(b) (2a – b)2
(c) (2a + b)2
(d) (2a –b2)

B

Question. The perimeter of a right triangle is 70cm and its hypotenuse is 29cm. The area of the triangle is
(a) 210 sq.cm
(b) 200 sq.cm
(c) 180 sq.cm
(d) 250 sq.cm

A

Question. 5x2 +8x +4 =2x2 +4x +6  is a
(b) cubic equation
(c) constant
(d) linear equation

A

Question. x2 – 30x + 225 = 0 have
(a) Real roots
(b) No real roots
(c) Real and Equal roots
(d) Real and Distinct roots

C

Question. If the quadratic equation bx2 -2√acx +b =0 has equal roots, then
(a) b2=-ac
(b) 2b2=ac
(c) b2=ac
(d) b2=2ac

C

Question. A quadratic equation ax2 +bx +c=0 has real and distinct roots, if
(a) b2 -4ac > 0
(b) b2 -4ac < 0
(c) None of these
(d) b2 -4ac =0

A

Question. 2x2 – 3x + 2 = 0 have
(a) Real and Distinct roots
(b) Real and Equal roots
(c) Real roots
(d) No Real roots

D

Question. 2x2 + 5√3 x + 6 = 0 have
(a) Real and equal root
(b) Real roots
(c) No Real roots
(d) Real and Distinct roots

D

Question. The value(s) of k, for which the roots of the equation 3x2 + 2k + 27 = 0 are real and equal are
(a) k = 9
(b) k = ± 9
(c) k = –9
(d) k = 0

B

Question. If one root of the equation (k − 1)x2 – 10x + 3 = 0 is the reciprocal of the other, then the value of k is
(a) 1
(b) 2
(c) 3
(d) 4

D

Question. The values of k for which the quadratic equation (k + 1)x2 + 2(k – 1)x + (k – 2) = 0 has equal roots, is:
(a) k = 2
(b) k = 3
(c) k = 0
(d) None of these

B

Question. If quadratic equation 3x2 – 4x + k = 0 has equal roots, then the value of k
(a) 1/3
(b) 2/3
(c) 3
(d) 4/3

D

Question. The value of k, for which the equation 2x2 – 10x + k = 0 has real roots is
(a) k ≤ 25/2
(b) k ≥ 25/2
(c) k = 25/2
(d) k > 25/2

A

Question. The value(s) of k for which the quadratic equation 2×2 + kx + 2 = 0 has equal roots, is
(a) 4
(b) ± 4
(c) – 4
(d) 0

B

Question. If the quadratic equation x2 – 2x + k = 0 has equal roots, then value of k is
(a) 1
(b) 2
(c) 3
(d) 0

A

Question. For what value of k, the equation 9x2 – 24x + k = 0 has equal roots?
(a) 12
(b) 16
(c) 18
(d) 20

B

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): The equation 8x2 + 3kx + 2 = 0 has equal roots, then the value of k is ± 8/3 .
Reason (R): The equation ax2 + bx + c = 0 has equal roots if D = b2 – 4ac = 0.

A

Question. Assertion (A): The roots of the quadratic equation x2 + 2x + 2 = 0 are imaginary.
Reason (R): If discriminant D = b2 – 4ac < 0, then the roots of quadratic equation ax2 + bx + c = 0 are imaginary.

A

Question. A cyclist takes 2 hours less to cover a distance of 200 km, if he increases his speed by 5 km/hr. Then his original speed is
(a) 26 km/hr
(b) 20 km/hr
(c) 24 km/hr
(d) 25 km/hr

B

Question. If the roots of the equation (a2 +b2)x2 -2ab (a+c) x +c2 +b2=0 are equal, then
(a) b=ac
(b) b2 =ac
(c) b =2ac/a+c
(d) 2b =a +c

B

Question. A quadratic equation ax2 +bx +c =0 has non – real roots, if
(a) b2 -4ac > 0
(b) b2 -4ac =0
(c) b2 -4ac < 0
(d) b2 -ac =0

C

Question. The quadratic equation whose roots are is
(a) 6x2 +13x -5=0
(b) 6x2 +13x +5=0
(c) 6x2 -13x +5=0
(d) 6x2 -13x -5=0

D

Question. If one root of the equation 4x2 -2x +(λ-4) =0 be the reciprocal of the other, then the value of λ is
(a) 8
(b) 4
(c) – 8
(d) – 4

A

(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.

Question. Assertion : (2x – 1)2 – 4x2 + 5 = 0 is not a quadratic equation.
Reason : x = 0, 3 are the roots of the equation 2x2 – 6x = 0.

B

Question. Assertion : Sum and product of roots of 2x2 – 3x + 5 = 0 are 3/ 2 and 5/ 2 respectively.
Reason : If α and β are the roots of ax2 + bx + c = 0, a ≠ 0, then sum of roots = α + β – b a = and product of roots αβ = c/a .

A

Question. Assertion : The equation 9x2 + 3kx + 4 = 0 has equal roots for k = ± 4.
Reason : If discriminant ‘D’ of a quadratic equation is equal to zero then the roots of equation are real and equal.

A

Question. Assertion : 4x2 – 12x + 9 = 0 has repeated roots.
Reason : The quadratic equation ax2 + bx + c = 0 have repeated roots if discriminant D > 0.

C

Question. Assertion : If roots of the equation x2 – bx + c = 0 are two consecutive integers, then b2 – 4c = 1.
Reason : If a, b, c are odd integer then the roots of the equation 4abc x2 + (b2 – 4ac) x – b = 0 are real and distinct.

B

Question. Assertion : A quadratic equation ax2 + bx + c = 0, has two distinct real roots, if b2 – 4ac > 0.
Reason : A quadratic equation can never be solved by using method of completing the squares.

C

One Word Questions :

Question. What are the nature of roots of the equation (x – 2a) (x – 2b) = 4ab?

real and distinct

Question. Find the solution set of quadratic equation : 5z² – 3z – 2 = 0.

{1 , -2/5}

Question. If S = n(n + 1)/2 = 78 , find n.

12

Question. What is the solution set of quadratic equation 2z² + az – a² = 0?

{- a ,a/2}

Question. For what value of p, the equation 4x² + 8x – p = 0 will have equal roots?

– 4

Question. There are three consecutive positive integers such that sum of, the square of the first and product of other two, is 29. What are the integers?

3, 4, 5

Question. The equation x² Kx p 0 have two roots –4 and –5. What is the value of K?

9

Question. What is the degree of the equation x(x² 3) 5 x³ 9x² 8.

2

Question. If , are the roots of the quadratic equation x² 2x – 8 0 , then what is the value of ² ² .

20

Question. Find two values of x which satisfy the quadractic equation x² – 64 = 0.

±8

Question. If x2 + 1/x2 = 2 , what are the values of x?

±1

Question. What is the value of D in the equation 9×2 +15x + 4 = 0 ?

81

Question. Divide 25 into two parts such that their product is 150.

15, 10

Question. Find two consecutive whole numbers, the difference of whose squares is 15.

7, 8

Question. What is the value of x in x + 3 /x = 4x ?

1 , -3/4

Question. For what value of p the quadratic equation, x² – 4x+ p = 0 , will have real and distinct roots?

p = 4

Question. What is the quadratic equation whose one of the roots is 3– √5 ?

x² – 6x + 4 = 0

Question. What is the quadratic equations whose roots are 3 and 4.

x² – 7x + 12 = 0

Question. What is the value of x which satisfies the equation √1 + 27/169 = 1+ x/13 ?

1

Question. Find the value of x which satisfies the equation : x + 4/x = –4; x 0

x = – 2

Question. For what value of k will the equation 5y² – 20y + (k – 1) = 0 have real and equal roots?

k = 21

Question. What will be the value of discriminant (D) if the given quadraric equation is perfect square?

0

Question. Determine the value of p for which the given quadratic equation has real roots :
2x² + 3x + p = 0

p ≤ 9/8

Question. Solve the quadratic equation : (x – 2)² – 25 = 0.