JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \(\alpha \), \(\beta \) and \(\gamma \) are three consecutive terms of a non-constant \(G.P.\) such that the equations \(\alpha x^2 + 2\beta x + \gamma = 0\) and \(x^2 + x -1 = 0\) have a common root, then \(\alpha(\beta + \gamma )\) is equal to
- A \(\alpha \gamma \)
- B \(0\)
- C \(\alpha \beta \)
- D \(\beta \gamma \)
Answer & Solution
Correct Answer
(D) \(\beta \gamma \)
Step-by-step Solution
Detailed explanation
\(\alpha, \beta, \gamma\) are in \(G.P.\) \(\alpha x^{2}+2 \beta x+\gamma=0\) and \(x^{2}+x-1=0\) have a common roots. Both roots will be common. \(\frac{\alpha}{1}=\frac{2 \beta}{1}=\frac{\gamma}{-1}=\lambda\)…
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