JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(\alpha\) and \(\beta\) be the roots of \(x^{2}-3 x+p=0\) and \(\gamma\) and \(\delta\) be the roots of \(x^{2}-6 x+q=0 .\) If \(\alpha\) \(\beta, \gamma, \delta\) form a geometric progression. Then ratio \((2 q+p):(2 q-p)\) is
- A \(3: 1\)
- B \(33: 31\)
- C \(9: 7\)
- D \(5: 3\)
Answer & Solution
Correct Answer
(C) \(9: 7\)
Step-by-step Solution
Detailed explanation
\(x^{2}-3 x+p=0<\beta\) \(\alpha, \beta, \gamma, \delta\) in G.P. \(\alpha+\alpha r=3 \ldots .(1)\) \(x^{2}-6 x+q=0<\frac{\gamma}{\delta}\) \(\alpha r^{2}+\alpha r^{3}=6 \quad \ldots(2)\) \((2) \div(1)\) \(r^{2}=2\) So,…
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