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If a, b are the roots of equation x^(2)-...

If a, b are the roots of equation `x^(2)-3x + p =0` and c, d are the roots of `x^(2) - 12x + q = 0` and a, b, c, d are in G.P., then prove that :
p : q =1 : 16

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To solve the problem step by step, we will analyze the given quadratic equations and the conditions provided. ### Step 1: Identify the roots and their relationships Given two quadratic equations: 1. \(x^2 - 3x + p = 0\) with roots \(a\) and \(b\) 2. \(x^2 - 12x + q = 0\) with roots \(c\) and \(d\) Since \(a, b, c, d\) are in geometric progression (G.P.), we can express them in terms of a common ratio \(r\): ...
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