CBSE Class 10 Mathematics Quadratic Equations MCQs Set B

Question: Two numbers whose sum is 12 and the absolute value of whose difference is 4 are the roots of the equation ________.
a) x² – 12x + 30 = 0
b) x² – 12x + 32 = 0
c) 2x² – 6x + 7 = 0
d) 2x² – 24x + 43 = 0
Answer: b

Question: If 2 is a root of the equation x² + bx + 12 = 0 and the equation x² + bx + q = 0 has equal roots, then q is equal to
a) 8
b) –8
c) 16
d) –16
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: For what value of a, the roots of the equation 2x² + 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: If one of roots of 2x² + 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: The roots of the equation x²/3 + x1/3 – 2 = 0 are ________.
a) 1, –8
b) 1, –2
c) 2/3, 1/3
d) –2, –8
Answer: a

Question: If x = √2 +√2 +√2 + ........... , then _______.
a) x = 1
b) 0 < x < 1
c) x is infinite
d) x = 2
Answer: d

Question: In the quadratic equation 9x² + 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: The roots of the equation 3x + 5 (x)^1/2 = √2 can be found by solving ________.
a) 9x² + 28x + 25 = 0
b) 9x² + 30x + 25 = 0
c) 9x² + 28x – 25 = 0
d) 16x² + 22x – 30 = 0
Answer: a

Question: The roots of ax₂ + bx + c = 0, a ≠ 0 are real and unequal, if b² – 4ac is _______.
a) = 0
b) > 0
c) < 0,
d) ≥ 0
Answer: b

Question: If one root of the equation a(b – c)x² + 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: 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: 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: Which of the following quadratic polynomials can be factorized into a product of real linear factors?
a) 2x² - 5x + 9
b) 2x² + 4x -5
c) 3x² + 4x + 6
d) 5x² - 3x + 2
Answer: b

Question: If the roots of the equation (a – b)x² + (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: 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: The ratio of the length and breadth of a rectangular photo frame is 3 : 2. Find its length if its area is 864 cm² .
a) 34 cm
b) 26 cm
c) 24 cm
d) 36 cm
Answer: d

Question: Find the value of 'p' for which m = 1/√3 is a root of the eq/uation pm² + ( √3 - √2)m - 1 = 0
a) √3
b) √2
c) √6
d) √7
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: If a and Rare the roots of the equation x² -8x + p = 0 such that α² + β² = 40 , find the value of 'p'.
a) 8
b) 10
c) 12
d) 14
Answer: c