Gate2019 cs Q57

0. Suppose Y is distributed uniformly in the open interval (1, 6). The probability that the polynomial 3x2 + 6xy + 3Y + 6 has only real roots is (rounded off to 1 decimal place) ________.

  • Option : A
  • Explanation :
    It is given that, Polynomial 3x2 + 6xY + 3Y + 6 has only real roots
    b2 – 4ax ≥ 0
    (6Y)2 – 4(3) (3Y+ 6) ≥ 0
    Y2 – Y - 2 ≥ 0<
    >Y ∈ (–∞, – 1] ∩ [2, ∞)
    ⇒ Y ∈ [2, 6)
    Since y is uniformly distributed in (1, 6)
    Probability distributed function,
    Gate2019 cs
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