JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(\alpha, \beta\) be the roots of the equation \(x^{2}-4 \lambda x+5=0\) and \(\alpha, \gamma\) be the roots of the equation \(x^{2}-(3 \sqrt{2}+2 \sqrt{3}) x+7+3 \lambda \sqrt{3}=0\). If \(\beta+\gamma=3 \sqrt{2}\), then \((\alpha+2 \beta+\gamma)^{2}\) is equal to
- A \(95\)
- B \(96\)
- C \(97\)
- D \(98\)
Answer & Solution
Correct Answer
(D) \(98\)
Step-by-step Solution
Detailed explanation
\(x^{2}-4 \lambda x+5=0\left\langle_{\beta}^{a}\right.\) \(x^{2}-(3 \sqrt{2}+2 \sqrt{3}) x+(7+3 \lambda \sqrt{3})=0\left\langle_{\gamma}^{\alpha}\right.\) \(\alpha+\beta=4 \lambda\) \(\alpha+\gamma=3 \sqrt{2}+2 \sqrt{3}\)…
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