CBSE Class 10 Mathematics Quadratic Equation Worksheet Set C

Question. Which of the following is a quadratic equation?
(a) x² + 2x + 1 = (4 − x)² + 3
(b) -2x² - (5 - x) (2x - 2/5)
(c) (k + 1) x² + 3/2 x = 7 , where k = −1
(d) x³ - x² = (x − 1)3
Answer : D

Question. Which of the following equation has root as 3?
(a) x² – 5x + 6 = 0
(b) – x² + 3x - 3 = 0
(c) √2x² - 3/√2 x + 1 = 0
(d) 3x² - 3x +3 = 0
Answer : A

Question. If b = 0, c < 0, then the roots of x² + bx + c = 0 are numerically equal and opposite in sign.
(a) True
(b) False
(c) Can’t determined
(d) None of these
Answer : A

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

Question. If 1/2 is a root of the equation x² + kx - 5/4 = 0, then the value of k is 
(a) 2
(b) −2
(c) 1/4
(d) 1/2
Answer : A

Question. The discriminant of the quadratic equationx x² − 4x + 1 = 0 is 
(a) 2√3
(b) 4
(c) 12
(d) 16
Answer : C

Question. 0.2 is a root of the equation x² − 0.4 = 0?
(a) True
(b) False
(c) Can’t determined
(d) None of these
Answer : B

Question. A quadratic equation with integral coefficient has integral roots.
(a) True
(b) False
(c) Can’t determined
(d) None of these
Answer : B

Question. If the discriminant of the equation kx² − 3√2x + 4√2 = 0 is 14, then the value of k is
(a) 2
(b) 1/3√2
(c) 1/√2
(d) 1/4√2
Answer : D

Question. The roots of the quadratic equation x² − 8x − 20 = 0 are
(a) 5, − 4
(b) − 4, 5
(c) 10, − 2
(d) − 10, 2
Answer : C

Question. Which constant must be added and subtracted to solve the quadratic equation 9x² + 3/4 x - √2 = 0.
(a) 1/8
(b) 1/64
(c) 1/4
(d) 9/64
Answer : B

Question. If a number x is added to twice its square, then the resultant is 21. Then the quadratic representation of this statement is
(a) 2x² - x + 21 = 0
(b) 2x² + x − 21 = 0
(c) 2x² - x − 20 = 0
(d) None of these
Answer : B

Question. A line segment AB is 8 cm in length. AB is produced to P such that BP2 = AB ⋅ AP. Then, the length of BP is
(a) 5(√5 + 1)
(b) √5 + 1
(c) 4(√5 + 1)
(d) √3 + 1
Answer : C

Question. If the discriminant of the equation 6x² - bx + 2 = 0 is 1, then the value of b is
(a) 7
(b) − 7
(c) Both (a) and (b)
(d) None of these
Answer :C 

Question. Value(s) of k for which the quadratic equation 2x² − kx + k = has equal roots is/are
(a) 0
(b) 4
(c) 8
(d) 0, 8
Answer : D

Question. Solve 12x² + 5x - 3 = 0.
(a) 1/3, 4/3
(b) 1/2, 3/4
(c) − 1/3, 3/4
(d) 1/3, − 3/4
Answer : D

Question. The quadratic equation 2x² = √5x + 1 = 0) has
(a) two distinct real roots
(b) two equal real roots
(c) no real roots
(d) more than 2 real roots
Answer : C

Question. Which of the following equations has two distinct real roots? [NCERT Exemplar]
(a) 2x² - 3√2x + 9/4 = 0
(b) x² + − 5 = 0
(c) x² + 3x + 2√2 = 0
(d) 5x² - 3x + 1 = 0
Answer : B

Question. Which of the following equations has no real roots?
(a) x² − 4x + 3√2 = 0
(b) x² + 4x − 3√2 = 0
(c) x² − 4x − 3√2 = 0
(d) 3x² + 4√3x + 4 = 0
Answer : A

Question. Which of the following is not a quadratic equation?
(a) 2 (x -1)² = 4x³ - 2x + 1
(b) 2x - x² = x² + 5
(c) (√2x + √3)² = 3x² – 5x
(d) (x² + 2x)² = x⁴ + 3 + 4x²
Answer : D

Question. The sum of the squares of three consecutive integers is 110, then the smallest positive integer is
(a) 6
(b) 5
(c) 7
(d) 4
Answer : B

Question. (x² + 1)² - x² − 0 has
(a) four real roots
(b) two real roots
(c) no real roots
(d) one real root
Answer : C

Question. One year ago, a man was 8 times as old as his son. Now, his age is equal to the square of his son’s age. Present age of man is
(a) 49 yr
(b) 37 yr
(c) 59 yr
(d) 39 yr
Answer : A

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