CBSE Class 10 Mathematics Quadratic Equations MCQs Set D

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

Answer: 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

Answer: B

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

Answer: 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

Answer: 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

Answer: 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

Answer: 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

Answer: 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 the options

Answer: 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

Answer: 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

Answer: D

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

Answer: 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

Answer: D

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

Answer: 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

Answer: A

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

Answer: 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

Answer: 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

Answer: 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)

Answer: B

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

Answer: 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

Answer: C

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

Answer: 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

Answer: D

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

Answer: 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

Answer: A

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

Answer: 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

Answer: A

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

Answer: C

One Word Questions :

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

Question. Find the solution set of quadratic equation : 5z² – 3z – 2 = 0.
Answer: {1 , -2/5}

Question. The equation x² Kx p 0 have two roots –4 and –5. What is the value of K?
Answer: 9

Question. What is the degree of the equation x(x² 3) 5 x³ 9x² 8.
Answer: 2

Question. What is the quadratic equations whose roots are 3 and 4.
Answer: x² – 7x + 12 = 0

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

Question. Solve the quadratic equation : (x – 2)² – 25 = 0.
Answer: x = –3, 7

Question. What are the two roots of 2x² – 7x = 0?
Answer: 0, 7/2

Question. What is the quadratic equation whose one of the roots is 3– √5 ?
Answer: x² – 6x + 4 = 0

Question. Find the value of x which satisfies the equation : x + 4/x = –4; x 0
Answer: x = – 2

Question. If S = n(n + 1)/2 = 78 , find n.
Answer: 12

Question. What is the solution set of quadratic equation 2z² + az – a² = 0?
Answer: {- a ,a/2}

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

Question. What is the value of D in the equation 9×2 + 15x + 4 = 0 ?
Answer: 81

Question. For what value of k will the equation 5y² – 20y + (k – 1) = 0 have real and equal roots?
Answer: k = 21

Question. What will be the value of discriminant (D) if the given quadraric equation is perfect square?
Answer: 0

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?
Answer: 3, 4, 5

Question. If , are the roots of the quadratic equation x² 2x – 8 0 , then what is the value of ² ² .
Answer: 20

Question. What is the value of x in x + 3 /x = 4x ?
Answer: 1 , -3/4

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

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

Question. Find two values of x which satisfy the quadractic equation x² – 64 = 0.
Answer: ±8

Question. Find two consecutive whole numbers, the difference of whose squares is 15.
Answer: 7, 8

Question. Determine the value of p for which the given quadratic equation has real roots : 2x² + 3x + p = 0
Answer: p ≤ 9/8

Question. Divide 25 into two parts such that their product is 150.
Answer: 15, 10