The number of positive integral values of k for which (16x^2+12x+39)+k(9x^2-2x+11) is a perfect square is

JEE Advanced Mathematics question

The number of positive integral values of for which

+12x+39)+-2x+11)

is a perfect square is

Answer: (B)

The expression is . A quadratic is a perfect square iff its discriminant is zero:

(12-=4(16+9k)(39+11k)(6-=(16+9k)(39+11k).

Expanding: (dividing by 49), i.e.

(2k+3)(k

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Question ID VK-108000