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Quadratic Equation Test - 7

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Quadratic Equation Test - 7
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Weekly Quiz Competition
  • Question 1
    1 / -0
    Which of the following equations has –84 as discriminant?
    Solution
    Discriminant = b2 - 4ac
    2x2 + 2x + 11 = 0
    D = 4 - 4 x 2 x 11
    = 4 - 88 = - 84
  • Question 2
    1 / -0
    Which of the following equations has as one of its solutions?
    Solution

    Put x =

    = Hence is a solution of
  • Question 3
    1 / -0
    Which of the following equations has -2 as one of its solutions?
    Solution
    (27 + 2)2 = 49
    y2 - 2 does not satisfy this
    (3y + 7)2 = 64
    y = - 2 does not satisfy this
    (y + 1)2 = 2
    y = -2 does not satisfy this.
    (4) option i : e None of these.
  • Question 4
    1 / -0
    Which of the following equations is same as 4x2 - 5x - 3 = 0?
    Solution
    4x2 - 5x - 3 = 0
    x2 - - = 0
    = 0

    Option (4)
  • Question 5
    1 / -0
    Which of the following equations has 8 as one of its solutions?
    Solution
    (x + 3)2 = 36
    x = 8 is not a solution
    (x - 3)2 = 25
    x = 8 gives
    52 = 25
    25 = 25
    Hence x = 8 is a solution to this equation.
  • Question 6
    1 / -0
    Which of the following equations has 9 as discriminant?
    Solution
    x2 + 5x + 4 = 0
    d = b2 - 4ac
    25 - 4 (4) 1
    = 25 - 16 - 9
    Option (1)
  • Question 7
    1 / -0
    Which of the following equations has real and equal roots?
    Solution
    3x2 - 17x + 20 = 0 for roots D = 0
    D = 289 - 240 = 49
    No equal roots.
    (2) 2x2 - 3x + 5 = 0
    D = 9 - 40 = - 31
    (3) 9x2 - 24x + 16 = 0
    d = 576 - 64 x 9
    = 576 - 576 = 0
    Hence real and equal roots.
  • Question 8
    1 / -0
    Which of the following equations has the solution y = 2?
    Solution
    (1) (2y + 1)2 = 25
    y = 2 satifies this
    (2) (3y - 1)2 = 25
    y = 2 satisfies this
    (3) (2y + 7)2 = 121
    y = 2 satisfies this
    (4) All of the above.
  • Question 9
    1 / -0
    Which of the following equations has no real roots?
    Solution
    For no real roots D < 0
    (1) D = 81 - 80 = 1 > 0
    (2) 196 - 4 (8) (-15) > 0
    (3) D = 324 - 320 > 0
    (4) D = 169 - 220 < 0
    Hence (4)
  • Question 10
    1 / -0
    What will be the discriminant of the given quadratic equation?
    3x2 + 5x + 2 = 0
    Solution
    3x2 + 5x + 2 = 0
    D = 25 - 24 = 1
  • Question 11
    1 / -0
    If the roots of the quadratic equation ax2 + bx + c = 0 are real and distinct, then _____.
    Solution
    ax2 + bx + c = 0
    b2 - 4ac > 0
  • Question 12
    1 / -0
    What will be the discriminant of the given quadratic equation?
    5x2 + x + 7 = 0
    Solution
    5x2 + x + 7 = 0
    D = 1 - 4 x 5 x 7
    = - 139
  • Question 13
    1 / -0
    Which of the following equations has (2 +) as one of its solutions?
    Solution
    (3x - 6)2 = 90
    3x - 6 =
    3x - 6 = 3
    x = 2 +
    Hence (1)
  • Question 14
    1 / -0
    What will be the discriminant of the given quadratic equation?
    2x2 + 7x + 5 = 0
    Solution
    2x2 + 7x + 5 = 0
    D = 49 - 4 x 2 x 5
    = 9
  • Question 15
    1 / -0
    If the roots of the quadratic equation ax2 + bx + c = 0 are real and equal, then ______.
    Solution
    ax2 + bx + c = 0 for equal and real D = 0
    D = b2 - 4ac = 0
  • Question 16
    1 / -0
    Which of the following equations can be obtained after completing the square of x2 + 6x + 3 = 0?
    Solution
    x2 + 6x + 3 = 0
    (x + 3)2 + 3 - 9 = 0
    (x + 3)2 = 6
  • Question 17
    1 / -0
    What will be the discriminant of the given quadratic equation?

    ax2 + bx + c = 0
    Solution
    ax2 + bx + c = 0
    b2 – 4ac
  • Question 18
    1 / -0
    Which of the following equations has no real roots?
    Solution
    x2 + x + 12 = 0
    D = 1 - 4 x (12)
    = - 47

    D < 0
    Hence no real root.
  • Question 19
    1 / -0
    Which of the following equations can be obtained after completing the square of x2 + 4x + 2 = 0?
    Solution
    x2 + 4x + 2 = 0
    (x + 2)2 + 2 - 4 = 0
    (x + 2)2 = 2
  • Question 20
    1 / -0
    Which of the following equations has 2 as one of its solutions?
    Solution
    (x - 2)2 = 0
    x = 2 satisfy this
  • Question 21
    1 / -0
    Which of the following equations can be obtained after completing the square of x2 + 9x + 7 = 0?
    Solution
    x2 + 9x + 7 = 0
    = 0
  • Question 22
    1 / -0
    Which of the following equations has real and distinct roots?
    Solution
    For real and distinct roots
    D = b2 - 4ac > 0
    (1) 25 - 20 > 0 Real and distinct roots
    (2) 144 - 16 > 0 Real and distinct roots
    (3) 25 - 8 > 0 Real and distinct roots
    All of the above
  • Question 23
    1 / -0
    Which of the following equations has as one of its solutions?
    Solution
    (2x + 3)2 = 100
    = 100
    (7 + 3)2 = 100
    (10)2 = 100
    100 = 100
  • Question 24
    1 / -0
    Which of the following equations can be obtained after completing the square of x2 + 4x - 1 = 0?
    Solution
    x2 + 4x - 1 = 0
    (x +2)2 - 1 - 4 = 0
    (x + 2)2 = 5
  • Question 25
    1 / -0
    If the quadratic equation ax2 + bx + c = 0 has no real roots, then ______.
    Solution
    b2 - 4ac < 0
  • Question 26
    1 / -0
    What will be the discriminant of the given quadratic equation?
    x2 + 7x - 1 = 0
    Solution
    x2 + 7x - 1 = 0
    D = 49 - 4 (1) (- 1)
    = 53
  • Question 27
    1 / -0
    Which of the following equations can be obtained after completing the square of x2 - 10x + 5 = 0?
    Solution
    x2 - 10x + 5 = 0
    (x - 5)2 + 5 - 25 = 0
    (x - 5)2 = 20
  • Question 28
    1 / -0
    Which of the following equations has real and distinct roots?
    Solution
    5x2 - 11x - 12 = 0
    D = 121 - 4 (5) (- 12)
    = 121 + 240 = 361 > 0
    Hence real and distinct roots
  • Question 29
    1 / -0
    Which of the following equations has -1 as one of its solutions?
    Solution
    (x + 5)2 = 10
    x = - 1 satisfy this
    (- 1 + 5)2 = 42 = 16
  • Question 30
    1 / -0
    Which of the following equations can be obtained after completing the square of 3x2 + 4x - 1 = 0?
    Solution
    3x2 + 4x - 1 = 0
    x2 + x - = 0
    = 0

    (3x + 2)2 = 7
  • Question 31
    1 / -0
    Which of the following quadratic equations has 0 as discriminant?
    Solution
    x2 + 4x + 4 = 0
    D = 16 - 4 x 4
    = 16 - 16 = 0
  • Question 32
    1 / -0
    Which of the following equations has 8 as one of its solutions?
    Solution
    (2x - 5)2 = 121
    x = 8 satisfies this
    (2 x 8 - 5)2 = (16 - 5)2 = 112 = 121
  • Question 33
    1 / -0
    Which of the following equations has no real roots?
    Solution
    7x2 - 3x + 5 = 0
    D = 9 - 140
    = - 131 hence no real roots.
  • Question 34
    1 / -0
    Which of the following equations can be obtained after completing the square of 3x2 - 11x - 4 = 0?
    Solution
    3x2 - 11x - 4 = 0
    x2 - x - = 0
    = 0
  • Question 35
    1 / -0
    Which of the following equations has 56 as discriminant?
    Solution
    (1) D = 16 - 56 = - 40
    (2) D = 64 + 8 = 72
    (3) = 64 - 8 = 56
  • Question 36
    1 / -0
    Which of the following equations has - as one of its solutions?
    Solution
    -as a solution?
    (x - 2)2 = 18
    (-)2
    (- 3)2
    9 x 2 = 18
  • Question 37
    1 / -0
    Which of the following equations has equal roots?
    Solution
    x2 + 4x + 4 = 0
    D = 16 - 16 = 0 has equal roots.
  • Question 38
    1 / -0
    Which of the following equations can be obtained after completing the square of 2x2 - 3x + 1 = 0?
    Solution
    2x2 - 3x + 1 = 0
    x2 - = 0
    = 0
  • Question 39
    1 / -0
    What will be the discriminant of the given quadratic equation?
    x2 + x + 1 = 2
    Solution
    x2 + x + 1 = 2
    x2 + x - 1 = 0
    D = 1 - 4 (- 1)
    = 5
  • Question 40
    1 / -0
    Which of the following equations can be obtained after completing the square of 3x2 + 7x + 2 = 0?
    Solution
    3x2 + 7x + 2 = 0
    x2 + = 0
    = 0
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