Applications of Quadratic Equations MCQ

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• If, x4 + 4x3 + 6ax2 + 6bx + c is divisible by x3 + 3x2 + 9x + 3. Then, what is the value of a + b + c?
  ক

  4

  খ

  6

  গ

  7

  ঘ

  10
• Let S denotes the set of all real values of the parameter ‘a’ for which every solution of the inequality log1/2 x2 ≥ log1/2 (x + 2) is the solution of the inequality 49x2 – 4a4 ≤ 0. What is the value of S? ∪
  ক

  (-∞, -√7) ∪ (√7, ∞) ∪ View Answer]

  খ

  (-∞, -√7
• For what value of θ, 1 lies between the roots of the quadratic equation 3x2 – 3sinθ x – 2cos2θ = 0?
  ক

  2nπ + π/6 < θ < 2nπ + 5π/6

  খ

  2nπ + π/3 < θ < 2nπ + 5π/3

  গ

  2nπ + π/6 ≤ θ ≤ 2nπ + 5π/6

  ঘ

  2nπ + π/3 ≤ θ ≤ 2nπ + 5π/3
• What is the set of values of p for which the roots of the equation 3x2 + 2x + p(p – 1) = 0 are of opposite sign?
  ক

  (-∞, 0)

  খ

  (0, 1)

  গ

  (1, ∞)

  ঘ

  (0, ∞)
• Which one is the complete set of values of x satisfying log x2 (x + 1) > 0?
  ক

  (1, ∞)

  খ

  (-1, 0) – {0}

  গ

  (-1, 1) – {0}

  ঘ

  (1, 0) ∪ (1, ∞)
• Which is the largest negative integer which satisfies (x2 – 1)/(x – 2)(x – 3)?
  ক

  -4

  খ

  -3

  গ

  -1

  ঘ

  -2
• What is the number of solution(s) of the equation |√x – 2| + √x(√x – 4) + 2 = 0?
  ক

  2

  খ

  4

  গ

  No solution

  ঘ

  Infinitely many solutions
• What will be the sum of the real roots of the equation x2 + 5|x| + 6 = 0?
  ক

  Equal to 5

  খ

  Equal to 10

  গ

  Equal to -5

  ঘ

  Does not exist
• What will be the value of f(x) if, 2A, A + B, C are integers and f(x) = Ax2 + Bx + C = 0?
  ক

  Natural Number

  খ

  Unpredictable

  গ

  Integer

  ঘ

  Complex Number
• If x1, x2 are real roots of ax2 – x + a = 0. Then, find the set of all values of parameter ‘a’ for which |x1 – x1| < 1?
  ক

  (1 – 5]/ a2 < 0 / a2 = 0 c) (1 – 5]/ a2 > 0 d) (1 – 5]/ a < 0 View Answer]

  খ

  (1 – 5a)/ a2 = 0

  গ

  (1 – 5a)/ a2 > 0

  ঘ

  (1 – 5a)/ a < 0