Highly selective Backlog Qs for JEE MainMathematicsQuadratic Equation

The number of real roots of the equation, e 4 x + e 3 x - 4 e 2 x + e x + 1 = 0 is:

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Correct answer

A. 1

Step-by-step solution

Let e x = t ∈ 0 , ∞ Given equation t 4 + t 3 - 4 t 2 + t + 1 = 0 t 2 + t - 4 + 1 t + 1 t 2 = 0 t 2 + 1 t 2 + t + 1 t - 4 = 0 Let t + 1 t = α α 2 - 2 + α - 4 = 0 α 2 + α - 6 = 0 α 2 + α - 6 = 0 α = - 3 , 2 ⇒ α = 2 ⇒ e x + e - x = 2 x = 0 only solutions

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