KVPY Government Jobs Exams

Let n be a natural number and let 'a' be a real number. The number of zeros of x^2n+1 – (2n + 1) x + a = 0 in the
interval [–1, 1] is –

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KVPY Other Question

The mid- point of the domain of the function f (x) =sqrt( 4 − 2x + 5) for real x is Let f : R → R be the function f(x) = (x – a1)(x–a2)+(x–a2)(x–a3) + (x– a3) (x–a1) with a1, a2, a3 ∈ R. Then f(x) > 0 if
and only if –
(A) At least two of a1, a2, a3 are equal (B) a1 = a2 = a3
(C) a1, a2, a3 are all distinct (D) a1, a2, a3 , are all positive and distinct