If one root of equation \(2x^2 - 10x + P = 0\) is 3, then the value of P is

Question

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:

Answer 1

Since 3 is a root, it satisfies the equation: \[ 2(3)^2 - 10(3) + P = 0 \] Simplification yields: \[ 18 - 30 + P = 0 \quad \Rightarrow \quad P = 12 \] Therefore, the answer is \(P = 12\).

If one root of equation \(2x^2 - 10x + P = 0\) is 3, then the value of P is

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The Correct Option is B

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