CBSE Class 10 Mathematics Quadratic Equations Assignment Set 01

Question. If the product of roots of the equation x³ – 3x + k = 10 is –2, then the value of k is
(a) –2
(b) –8
(c) 8
(d) 12

Answer: C

Question. If one root of 5x² + 13x + k = 0 be the reciprocal of the other root, then the value of k is
(a) 0
(b) 1
(c) 2
(d) 5

Answer: D

Question. If the sum of the roots of a quadratic equation is 6 and their product is 6, the equation is
(a) x² – 6x + 6 = 0
(b) x² + 6x – 6 = 0
(c) x² – 6x – 6 = 0
(d) x² + 6x + 6 = 0

Answer: A

Question. Find the product of the roots of x² + 8x – 16 = 0
(a) 8
(b) –8
(c) 16
(d) –16

Answer: D

Question. If the roots of the equation ax² + bx + c = 0 are α and β, then the quadratic equation whose roots are –α and –β is _____ .
(a) ax² – bx – c = 0
(b) ax² – bx + c = 0
(c) ax² + bx – c = 0
(d) ax² – bx + 2c = 0

Answer: B

Question. If the equation (1 + m²) x² + (2mc) x + (c² – a²) = 0 has equal roots, then
(a) c² – a² = 1 +m²
(b) c² = a² (1 + m²)
(c) c²a² = (1 + m²)
(d) c² + a² = 1 + m²

Answer: B

Question. Which of the following satisfy the equation a²b²x² + b²x – a²x – 1 = 0
(a) 1/a²
(b) 1/b²
(c) -1/b²
(d) None of these

Answer: B

Question. The roots of the quadratic equation x² – 0.04 = 0 are
(a) ± 0.2
(b) ± 0.02
(c) 0.4
(d) 2

Answer: A

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 x² 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 the equation x² + 2(k + 2)x + 9k = 0 has equal roots, then k = ?
(a) 1 or 4
(b) –1 or 4
(c) 1 or – 4
(d) –1 or – 4

Answer: A

Question. If the roots of 5x² – kx + 1 = 0 are real and distinct, then
(a) −2√5 < k < 2√5
(b) k > 2√5 only
(c) k < −2√5 only
(d) either k > 2√5 or k < −2√5

Answer: D

Question. If a – b, b – c are the roots of ax² + bx + c = 0, then find the value of (a - b)(b - c)/c - a
(a) b/c
(b) c/b
(c) ab/c
(d) bc/a

Answer: B

Question. The condition for one root of the quadratic equation ax² + bx + c = 0 to be twice the other, is
(a) b² = 4ac
(b) 2b² = 9ac
(c) c² = 4a + b²
(d) c² = 9a – b²

Answer: B

Question. If the ratio of the roots of the equation x² + bx + c = 0 is the same as that of x² + qx + r = 0, then
(a) r²b = qc²
(b) r²c = qb²
(c) c2r = q²b
(d) b²r = q²c

Answer: D

Question. The real roots of the equation x²/³ + x^1/3 − 2 = 0 are
(a) 1, 8
(b) –1, –8
(c) –1, 8
(d) 1, –8

Answer: D

Question. Which of the following is not a quadratic equation?
(a) x² – 2x + 2 (3 – x) = 0
(b) x (x + 1) + 1 = (x – 2) (x – 5)
(c) (2x – 1) (x – 3) = (x + 5) (x – 1)
(d) x³ – 4x² – x + 1 = (x –2)³

Answer: B

Question. If one root of the quadratic equation ax² + bx + c = 0 is the reciprocal of the other, then
(a) b = c
(b) a = b
(c) ac = 1
(d) a = c

Answer: D

Question. The roots of the equation x + 1/x  = 3(1/3), x ≠ 0, are
(a) 3, 1
(b) 3, 1/3
(c) 3, − (1/3)
(d) – 3, 1/3

Answer: B

Question. If the equation (m² + n²) x² –2 (mp + nq) x + p² + q² = 0 has equal roots, then
(a) mp = nq
(b) mq = np
(c) mn = pq
(d) mq = √np

Answer: B

Question. If x² + y² = 25, xy = 12, then x =
(a) {3, 4}
(b) {3, –3}
(c) {3, 4, –3, –4}
(d) {–3, –3}

Answer: C

Question. If x = √ 7 + 4√3 , then x + 1/x =
(a) 4
(b) 6
(c) 3
(d) 2

Answer: A

Question. If the roots of the equation px² + 2qx + r = 0 and qx² − 2√prx + q = 0 be real, then
(a) p = q
(b) q² = pr
(c) p² = qr
(d) r² = pq

Answer: B

Question. The equation 2x² + 2(p + 1) x + p = 0, where p is real, always has roots that are
(a) Equal
(b) Equal in magnitude but opposite in sign
(c) Irrational
(d) Real

Answer: D

Question. Each root of x² – bx + c = 0 is decreased by 2. The resulting equation is x² – 2x + 1 = 0, then
(a) b = 6, c = 9
(b) b = 3, c = 5
(c) b = 2, c = –1
(d) b = – 4, c = 3

Answer: A

Question. Two distinct polynomials f (x) and g(x) are defined as follows:
f (x) = x² + ax + 2; g (x) = x² + 2x + a.
If the equations f (x) = 0 and g(x) = 0 have a common root, then the sum of the roots of the equation f (x) + g(x) = 0 is
(a) - (1/2)
(b) 0
(c) 1/2
(d) l

Answer: C

Question. If a and b are the roots of the quadratic equation x² – 6x – 2 = 0 and if a_n = α_n – β_n, then the value of a₁₀ - 2a₈/2a₉ is
(a) 6.0
(b) 5.2
(c) 5.0
(d) 3.0

Answer: D

Question. If x = 3 + √5 / 2 and y = x³, then y satisfies the quadratic equation
(a) y² – 18y + 1 = 0
(b) y² + 18y + 1 = 0
(c) y² – 18y – 1 = 0
(d) y² + 18y – 1 = 0

Answer: A

Question. Let b be a non-zero real number. Suppose the quadratic equation 2x² + bx + 1/b = 0 has two distinct real roots. Then
(a) b + 1/b > 5/2
(b) b + 1/b < 5/2
(c) b² – 3b > –2
(d) b² + 1/b² < 4

Answer: C

Question. If the quadratic equations 2x² + 4x + (a + 5) = 0 have equal roots and (a + 4)x² + ax – 3b = 0 have distinct real roots then which of the following is true:
(a) a = –3, b < 3/4
(b) a = 3, b > 3/4
(c) a = –3, b > – 3/4
(d) a = 3, b < 3/4

Answer: C

Question. The value of λ such that sum of the squares of the roots of the quadratic equation, x² + (3 – l)x + 2 = λ has the least value is:
(a) 15/8
(b) 1
(c) -
(d) 2

Answer: D

Question. Consider the quadratic equation nx² + 7√nx + n = 0, where n is a positive integer. Which of the following statements are necessarily correct?
I. For any n, the roots are distinct.
II. There are infinitely many values of n for which both roots are real.
III. The product of the roots is necessarily an integer.
(a) III only
(b) I and III
(c) II and III
(d) I, II and III

Answer: B

Question. Two quadratic equations x² – bx + 6 = 0 and x² – 6x + c – 0 have a common root. If the remaining roots of the first and second equations are positive integers and are in the ration 3 : 4 respectively, then the common root is
(a) 1
(b) 2
(c) 3
(d) 4

Answer: B

Question. The values of k, so that the equations 2x² + kx – 5 = 0 and x² – 3x – 4 = 0 have one root in common, are
(a) 3, 27/2
(b) 9, 27/4
(c) – 3, −27/4
(d) 3, 4/27

Answer: C

Question. If α and β be two roots of the equation x² – 64x + 256 = 0.
Then the value of (α³/β⁵)^1/8 + (β³/α⁵)^1/8 is:
(a) 2
(b) 3
(c) 1
(d) 4

Answer: A

Question. Which one of the following is not a quadratic equation?
(a) (x + 2)² = 2(x + 3)
(b) x² + 3x = (–1) (1 – 3x)²
(c) (x + 2) (x – 1) = x² – 2x – 3
(d) x³ – x² + 2x + 1 = (x + 1)³

Answer: C

Question. If equation x² – (2 + m) x + 1 (m2 – 4m + 4) = 0 has equal roots, then:
(a) m = 0
(b) m = 6
(c) m = 2
(d) m = 3

Answer: B

Question. Which of the following equations have no real roots?
(a) x² − 2√3x + 5 = 0
(b) 2x² + 6√2 +8 = 0
(c) x² − 2√3x − 5 = 0
(d) 2x² − 6√2x − 9 = 0

Answer: A

Question. Two numbers whose sum is 8 and the absolute value of whose difference is 10 are roots of the equation
(a) x² – 8x + 9 = 0
(b) x² – 8x – 9 = 0
(c) x² + 8x – 9 = 0
(d) –x² + 8x + 9 = 0

Answer: B

Question. If α, β are roots of x² + 5x + a = 0 and 2α + 5β = –1, then
(a) α = 8
(b) β = –3
(c) α = 9
(d) a = – 24

Answer: D

Question. Which constant should be added and subtracted to solve the quadratic equation 4x² – √3x – 5 = 0 by the method of completing the square?
(a) 9/16
(b) 3/64
(c) 3/4
(d) √3/4

Answer: B

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

Answer: C

Question. Values of k for which the quadratic equation 2x²– kx + k = 0 has equal roots is
(a) 0 only
(b) 4 only
(c) 8 only
(d) 0, 8

Answer: D

Question. If α, β are roots of the equation x² – 5x + 6 = 0, then the equation whose roots are α + 3 and β + 3 is
(a) 2x² – 11x + 30 = 0
(b) –x² + 11x = 0
(c) x² – 11x + 30 = 0
(d) 2x² – 22x + 40 = 0

Answer: C

Question. The value of p for which the difference between the roots of the equation x² + px + 8 = 0 is 2, are
(a) 4
(b) 8
(c) 6
(d) – 4

Answer: C

Question. If the roots of x² + px + 12 = 0 are in the ratio 1 : 3, then value(s) of p are
(a) 3
(b) 8
(c) 6
(d) – 3

Answer: B

Question. Roots of quadratic equation x² – 3x + 2 = 0 are
(a) 3
(b) –1
(c) 2
(d) 4

Answer: C

Question. If x = 2 and x = 3 are roots of the equation 3x² – 2px + 2q = 0, then
(a) P = 2/15
(b) p = 15
(c) q = 9
(d) 6p + 2q = 27

Answer: C

Fill in the Blanks

DIRECTIONS : Complete the following statements with an appropriate word/ term to be filled in the blank space(s).

Question. A quadratic equation in the variable x is of the form ax² + bx + c = 0, where a, b, c are real numbers and a ......
Answer: ≠ 0

Question. A quadratic equation ax² + bx + c = 0 has two distinct real roots, if b² – 4ac ..............
Answer: > 0

Question. The values of k for which the equation 2x² + kx + x + 8 = 0 will have real and equal roots are .............
Answer: 7 and –9

Question. The quadratic equation whose roots are the sum and difference of the squares of roots of the equation x² – 3x + 2 = 0 is....
Answer: x² – 8x + 15 = 0

Question. If a, b are the roots of x² + x + 1 = 0, then a2 + b2 = ...........
Answer: –1

Question. If α, β are the roots of x² + bx + c = 0 and α + h, β + h are the roots of x² + qx + r = 0, then h = ..........
Answer: 1/2 (b - q)

Question. If α, β are roots of the equation ax² + bx + c = 0, then the quadratic equation whose roots are aα + b and aβ + b is .............
Answer: x² – bx + ca = 0

Question. If r, s are roots of ax² + bx + c = 0, then is  1/r² + 1/r² is ..........
Answer: b² - 2ac/c²

Question. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, the other two sides are ...............
Answer: 5 cm, 12 cm.

Question. The equation ax² + bx + c = 0, a ≠ 0 has no real roots, if .........
Answer: b² < 4ac

Question. A quadratic equation cannot have more than ........ roots.
Answer: two

Question. Let ax² + bx + c = 0, where a, b, c are real numbers, a ≠ 0, be a quadratic equation, then this equation has no real roots if and only if ........... 
Answer: b² < 4ac

Please click the link below to download CBSE Class 10 Mathematics Quadratic Equations Assignment Set A