Let α and β be the roots of the equation x2−x+p=0 and let γ and δ be the roots of the equation x2−4x+q=0. If α,β,γ,δ are in Geometric progression then what is the value of p and q?
My approach:
From the two equations,
α+β=1,
αβ=p,
γ+δ=4, and,
γδ=q.
Since α,β,γ,δ are in G. P., let α=ar3, β=ar1, γ=ar,
δ=ar3.
∴
Now,
\frac{\alpha + \beta}{\gamma + \delta} = \frac{1}{r^4}
\frac{1}{4} = \frac{1}{r^4}
\therefore r = \sqrt(2)
From here I don't know how to proceed. Am I unnecessarily complicating the problem??
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