If a is an integer lying in [−5,30], then the probability that the graph of y=x2+2(a+4)x−5a+64 is strictly above the x-axis is

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1/6

7/36

2/9

3/5

answer is C.

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Detailed Solution

x2+2(a+4)x−5a+64≥0 If D≤0, then (a+4)2−(−5a+64)<0OR a2+13a−48<0OR (a+16)(a−3)<0⇒−16

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