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Question

If the roots of the cubic equation ax3+bx2+cx+d=0 are in G.P., then

A
c3a=b3d
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B
ca3=bd3
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C
a3b=c3d
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D
ab3=cd3
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Solution

The correct option is A c3a=b3d
Roots of the cubic equation ax3+bx2+cx+d=0 are in G.P.
Let the roots be AR,A,AR

Product of roots =da=AR×A×AR

=>da=A3 ---- Equation 1

Sum of roots =ba=AR+A+AR

=>ba=A(1+R+R2R) ----Equation 2

Sum of product of roots taking 2 at a time =ca=A2R+A2R+A2

=>ca=A2(1+R+R2R) ----Equation 3

Dividing equation 3 by equation 2, we get
cb=A ----Equation 4

From equation 1 and equation 4, we get
da=(cb)3

=>da=c3b3

=>c3a=b3d


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