If `a\ a n d\ b` are the roots of `x^2-3x+p=0\ a n d\ c ,\ d` are the roots `x^2-12 x+q=0` where `a , b , c , d` form a G.P. Prove that `(q+p):(q-p)=17 : 15.`

Explanation

To solve the problem, we need to prove that \((q + p):(q - p) = 17:15\) given that \(a, b, c, d\) are roots of two quadratic equations and they form a geometric progression (G.P.).

### Step 1: Identify the roots and their relationships
Given:
1. \(a\) and \(b\) are roots of the equation \(x^2 - 3x + p = 0\).
2. \(c\) and \(d\) are roots of the equation \(x^2 - 12x + q = 0\).
3. \(a, b, c, d\) are in G.P.

...