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Question

If roots of the equation
x48x3+bx2+cx+16=0
are positive, then


A

b=8

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B

c=-32

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C

b=24

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D

c=32

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Solution

The correct option is C

b=24


If x1,x2,x3,x4 are four roots of (1), then
x1+x2+x3+x4=8and x1 x2 x3 x4=16
As A.M. G.M., we get
14(x1+x2+x3+x4)(x1 x2 x3 x4)1/4=2i.e. A.M.=G.M.Thus, x1=x2=x3=x4=2x48x3+bx2+cx+16=(x2)4b=24 and c=32


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