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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:

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In root-based problems, converting reciprocal conditions into expressions involving sum and product simplifies the algebra.

Updated On: Apr 1, 2026

$8$
$6$
$4$
$2$

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The Correct Option is B

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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:

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The Correct Option is B

Solution and Explanation

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