JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \(\alpha\) and \(\beta\) are the roots of the equation, \(7 x^{2}-3 x-2=0,\) then the value of \(\frac{\alpha}{1-\alpha^{2}}+\frac{\beta}{1-\beta^{2}}\) is equal to
- A \(\frac{27}{16}\)
- B \(\frac{1}{24}\)
- C \(\frac{27}{32}\)
- D \(\frac{3}{8}\)
Answer & Solution
Correct Answer
(A) \(\frac{27}{16}\)
Step-by-step Solution
Detailed explanation
\(7 x^{2}-3 x-2=0\) \(\alpha+\beta=\frac{3}{7} \quad \alpha \beta=\frac{-2}{7}\) \(\frac{\alpha}{1-\alpha^{2}}+\frac{\beta}{1-\beta^{2}}=\frac{\alpha+\beta-\alpha \beta(\alpha+\beta)}{1-\alpha^{2}-\beta^{2}+\alpha^{2} \beta^{2}}\)…
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