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Question

If the roots of the cubic equation ax3+bx2+cx+d=0 are in G.P. then
  1. c3a=b3d
     
  2. ca3=bd3
     
  3. a3b=c3d
     
  4. ab3=cd3
     


Solution

The correct option is A c3a=b3d
 
Let AR,A,AR be the roots of the equation ax3+bx2+cx+d=0.
Then A3 = product of the roots = da
A=(da)13
Since A is a root of the equation, aA3+bA2+cA+d=0
a(da)+b(da)23+c(da)13+d=0
b3d2a2=c3da
b3d=c3a

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