The smallest value of k, for which both the roots of the equation x^2 - 8kx + 16(k^2 - k + 1) = 0 are real, distinct and have values at least 4, is

JEE Advanced 2009 Mathematics question

The smallest value of k, for which both the roots of the equation

- 8kx + - k + 1) = 0

are real, distinct and have values at least 4, is

Answer: 2

Distinct real roots: . Both roots ≥ 4 requires f(4) ≥ 0 and the vertex 4k > 4: $f(4)

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Question ID VK-037767