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Question

If aI and a[5,30] then the probability that the graph of y=x2+2(a+4)x5a+64 is strictly above the x-axis is

A
16
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B
736
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C
12
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D
35
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Solution

The correct option is C 12
Given aI and a[5,30]
y=x2+2(a+4)x5a+64
a can assume values from 5 to 30.
y=x2+2(a+4)x5a+64>0 for all aI and xR
disc<0 i.e, b24c<0
=[2(a+4)]24[(5a+64)]
=a2+18a+144.
The roots are (a,a), this point denotes that the graph is below xaxis.
The probability of rest of points being strictly above the xaxis =12.
Hence, the answer is 12.


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