JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(\alpha, \beta\) be the roots of the equation \(x^2 - x + p = 0\) and \(\gamma, \delta\) be the roots the equation \(x^2 - 4x + q = 0\); \(p, q \in \mathbf{Z}\). If \(\alpha, \beta, \gamma, \delta\) are in G.P., then \(|p + q|\) equals :
- A \(16\)
- B \(32\)
- C \(34\)
- D \(38\)
Answer & Solution
Correct Answer
(C) \(34\)
Step-by-step Solution
Detailed explanation
Let \(\alpha = a, \beta = ar, \gamma = ar^2, \delta = ar^3\) be the terms of the G.P. From the given quadratic equations, the sum of the roots are: \(\alpha + \beta = 1 \Rightarrow a(1 + r) = 1\) \(\gamma + \delta = 4 \Rightarrow ar^2(1 + r) = 4\) Dividing the second equation by…
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