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Question

The roots of the equation x48x3+ax2bx+16=0, are positive, if

A
a=24
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B
a=12
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C
b=8
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D
b=32
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Solution

The correct option is A a=24
x48x3+ax2bx+16=0
α1+α2+α3+α4=8
α1α2α3α4=16
AM=GM=2
Dividing from AMGM inequality
(n1i=1n(ni=1ai)1/n)
Only when all the terms are equal .
Hence all roots are equal
So α1=α2=α3=α4=2
So, A and B are true


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