Question:
The positive numbers \(\alpha\) and \(\beta\) have geometric mean 6. If \(\alpha\) and \(\beta\) are roots of the equation \(2x^{2} - 25x + \lambda = 0\) then the value of \(\lambda\) is equal to
The positive numbers \(\alpha\) and \(\beta\) have geometric mean 6. If \(\alpha\) and \(\beta\) are roots of the equation \(2x^{2} - 25x + \lambda = 0\) then the value of \(\lambda\) is equal to
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For \(ax^2+bx+c=0\), product = \(c/a\).
Updated On: Apr 25, 2026
- 6
- 36
- 12
- 72
- 48
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
Geometric mean \(= \sqrt{\alpha\beta} = 6 \implies \alpha\beta = 36\). For quadratic \(2x^2 - 25x + \lambda = 0\), product of roots = \(\lambda/2\). So \(\lambda/2 = 36 \implies \lambda = 72\).
Step 2: Detailed Explanation:
No further steps.
Step 3: Final Answer:
Option (D).
Geometric mean \(= \sqrt{\alpha\beta} = 6 \implies \alpha\beta = 36\). For quadratic \(2x^2 - 25x + \lambda = 0\), product of roots = \(\lambda/2\). So \(\lambda/2 = 36 \implies \lambda = 72\).
Step 2: Detailed Explanation:
No further steps.
Step 3: Final Answer:
Option (D).
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