JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \(\alpha, \beta,\) where \(\alpha<\beta\), are the roots of the equation \(\lambda x^{2}-(\lambda+3)x+3=0\) such that \(\frac{1}{\alpha}-\frac{1}{\beta}=\frac{1}{3},\) then the sum of all possible values of \(\lambda\) is:
- A 6
- B 2
- C 4
- D 8
Answer & Solution
Correct Answer
(A) 6
Step-by-step Solution
Detailed explanation
\(\frac{\beta-\alpha}{\alpha\beta}=\frac{1}{3}, \alpha+\beta=\frac{\lambda+3}{\lambda}, \alpha\beta=\frac{3}{\lambda}\) \(\beta-\alpha=\frac{\alpha\beta}{3}=\frac{1}{\lambda}\) on squaring \(\alpha^{2}+\beta^{2}-2\alpha\beta=\frac{1}{\lambda^{2}}\) ........(1)…
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