1.

Let alpha + beta = 1, 2 alpha^(2) + 2beta^(2) = 1 and f(x) be a continuous function such that f(2 + x) + f(x) = 2 for all x in [0, 2] and p = int_(0)^(4) f(x) dx - 4, q = (alpha)/(beta). Then, find the least positive integral value of 'a' for which the equation ax^(2) - bx + c = 0 has both roots lying between p and q, where a, b, c in N.

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ANSWER :a = 5


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