JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \(\alpha\) and \(\beta\) are the roots of the equation \(x ^{2}+ px +2=0\) and \(\frac{1}{\alpha}\) and \(\frac{1}{\beta}\) are the roots of the equation \(2 x^{2}+2 q x+1=0,\) then \(\left(\alpha-\frac{1}{\alpha}\right)\left(\beta-\frac{1}{\beta}\right)\left(\alpha+\frac{1}{\beta}\right)\left(\beta+\frac{1}{\alpha}\right)\) is equal to
- A \(\frac{9}{4}\left(9+ p ^{2}\right)\)
- B \(\frac{9}{4}\left(9-q^{2}\right)\)
- C \(\frac{9}{4}\left(9-p^{2}\right)\)
- D \(\frac{9}{4}\left(9+q^{2}\right)\)
Answer & Solution
Correct Answer
(C) \(\frac{9}{4}\left(9-p^{2}\right)\)
Step-by-step Solution
Detailed explanation
\(\alpha, \beta\) are roots of \(x^{2}+p x+2=0\) \(\Rightarrow \alpha^{2}+p \alpha+2=0 \& \beta^{2}+p \beta+2=0\) \(\Rightarrow \frac{1}{\alpha}, \frac{1}{\beta}\) are roots of \(2 x ^{2}+ px +1=0\) But \(\frac{1}{\alpha}, \frac{1}{\beta}\) are roots of \(2 x^{2}+2 q x+1=0\)…
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