JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(\lambda \neq 0\) be a real number. Let \(\alpha, \beta\) be the roots of the equation \(14 x^2-31 x+3 \lambda=0\) and \(\alpha, \gamma\) be the roots of the equation \(35 x^2-53 x+4 \lambda=0\). Then \(\frac{3 \alpha}{\beta}\) and \(\frac{4 \alpha}{\gamma}\) are the roots of the equation :
- A \(7 x ^2+245 x -250=0\)
- B \(7 x ^2-245 x +250=0\)
- C \(49 x ^2-245 x +250=0\)
- D \(49 x^2+245 x+250=0\)
Answer & Solution
Correct Answer
(C) \(49 x ^2-245 x +250=0\)
Step-by-step Solution
Detailed explanation
\(14 x^2-31 x+3 \lambda=0\) \(\alpha+\beta=\frac{31}{14} \ldots .(1) \text { and } \alpha \beta=\frac{3 \lambda}{14} \ldots .(2)\) \(35 x^2-53 x+4 \lambda=0\) \(\alpha+\gamma=\frac{53}{35} \ldots(3) \text { and } \alpha \gamma=\frac{4 \lambda}{35} \ldots(4)\)…
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