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Question

If the roots of px3+qx2+rx+s=0are in A.P., then the roots of 8px3+4qx2+2rx+s=0 are in

A
A.P.
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B
G.P
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C
H.P.
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D
A.G.P.
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Solution

The correct option is A A.P.
Let α,β,γ be roots of px3+qx2+rx+s=0
Now replacing x2x, we get
p(2x)3+q(2x)2+r(2x)+s=08px3+4qx2+2rx+s=0
So α2,β2,γ2 are roots of 8px3+4qx2+2rx+s=0
Now as α,β,γ are in A.P
then α2,β2,γ2 are also in A.P

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