Properties of nth Root of a Complex Number

Let S=a ∈ N, ...

Question

Let $S = {a \in N, a \leq 100}$ . If the equation $[T a n^{2} x] - T a n x - a = 0$ has real roots then number of elements in S is (where [] is step functin).

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Solution

The correct option is C
9

Given equation is true only when Tanx is an integer $T a n x = \frac{1 \pm \sqrt{4 a + 1}}{2} = 4 a + 1$ is perfect square and $4 a + 1 \leq 401$

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