The probability of selecting integers a ∈ [−5, 30] such that x^2 + 2(a + 4)x − 5a + 64 0, for all x ∈ R, is:

Question

The probability of selecting integers a ∈ [−5, 30] such that x^2 + 2(a + 4)x − 5a + 64 > 0, for all x ∈ R, is:

Accepted Answer

Correct answer: B. (b) D < 0 ⇒ 4(a + 4)^2 − 4(−5a + 64) < 0 ⇒ a^2 + 16 + 8a + 5a − 64 < 0 ⇒ a^2 + 13a − 48 < 0 ⇒ (a + 16)(a − 3) < 0 ⇒ a ∈ (−16, 3) ∴Possible a : −5,−4,……, 3 ∴Required probability = 83 6= 29

$The probability of selecting integers a \in [-5, 30] such that x^{2} + 2(a + 4)x - 5a + 64 > 0, for all x \in R, is:$

Solution

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