QJEEM21Maaf8d: JEE Main 2021 Mathematics - Class 12 JEEM21Maaf8d Solution: The number of real roots of the equation e 4 x + 2 e 3 x − e x…

Question

Verified Solution • 2025–26 Session moderate

The number of real roots of the equation

e^{4 x} + 2 e^{3 x} - e^{x} - 6 = 0

is :

Accepted Answer

Let

e^{x} = t > 0

f (t) = t^{4} + 2 t^{3} - t - 6 = 0

f^{'} (t) = 4 t^{3} + 6 t^{2} - 1

f^{″} (t) = 12 t^{2} + 12 t > 0

f (0) = - 6, f (1) = - 4, f (2) = 24

\Rightarrow

Number of real roots = 1

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