JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \(\lambda \) be the ratio of the roots of the quadratic equation in \(x, 3m^2x^2 + m(m -4)x + 2 = 0\), then the least value of \(m\) for which \(\lambda + \frac{1}{\lambda } = 1\), is
- A \(2 - \sqrt 3 \)
- B \(4 - 3\sqrt 2 \)
- C \(-2 + \sqrt 2 \)
- D \(4 - 2\sqrt 3 \)
Answer & Solution
Correct Answer
(B) \(4 - 3\sqrt 2 \)
Step-by-step Solution
Detailed explanation
Let roots are \(\alpha\) and \(\beta\) now \(\lambda+\frac{1}{\lambda}=1 \Rightarrow \frac{\alpha}{\beta}+\frac{\beta}{\alpha}=1\) \(\Rightarrow \alpha^{2}+\beta^{2}=\alpha \beta\) \((\alpha+\beta)^{2}=2 \alpha \beta\)…
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