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if alpha , beta be roots of x^2-3x+a=0 ...

if `alpha , beta ` be roots of `x^2-3x+a=0` and `gamma , delta ` are roots of `x^2-12x+b=0` and `alpha,beta,gamma,delta`(in order) form a increasing GP then find the value of `a & b`

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` alpha, beta,gamma ,delta ` are in GP so assume them to be `a,ar,ar^2,ar^3` where a is the first term and r common ratio
. also`alpha +beta=a+ar=3`...(1) and `gamma+delta=ar^2+ar^3=12`...(2)
dividing (2) by(1) we get=>`r^2=4,r=2`
from(1) we get a=1
thus by product of roots formula we get
=>`a^2r=A=2`
=>`a^2r^5=B=32`
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