if a, b are the roots of x^2 - 3x + p =0 and c, d are the roots of x^2 - 12x +q = 0 where a,b,c,d form a G.P, find the ratio of (q+p):(q-p)

It is given that a and b are the roots of x² – 3x + p = 0

a + b = 3 and ab = p … (1)

Also, c and d are the roots of

c + d = 12 and cd = q … (2)

It is given that a, b, c, d are in G.P.

Let a = x, b = xr, c = xr², d = xr³

From (1) and (2), we obtain

x + xr = 3

 x (1 + r) = 3

xr² + xr³ =12

 xr² (1 + r) = 12

On dividing, we obtain

When r = 2 and x =1,

ab = x²r = 2

cd = x²r⁵ = 32

similarly when  r = -2 & x =  -3  wecan do it by getting same result