Verified Solution • 2025–26 Session moderate

QJEEM21Ma5c79: JEE Main 2021 Mathematics - Class 11 JEEM21Ma5c79 Solution: The number of real roots of the equation e 4x e 3x 4e 2x e x +…

The number of real roots of the equation e4x −- e3x −- 4e2x −- ex + 1 = 0 is equal to ______________.

Step-by-Step Verified Solution

t4 −- t3 −- 4t2 −- t + 1 = 0, ex = t > 0

⇒t2−t−4−1t+1t2=0\Rightarrow {t^2} - t - 4 - {1 \over t} + {1 \over {{t^2}}} = 0

⇒α2−α−6=0,α=t+1t≥2\Rightarrow {\alpha ^2} - \alpha - 6 = 0,\alpha = t + {1 \over t} \ge 2

⇒α=3,−2\Rightarrow \alpha = 3, - 2 (reject)

⇒t+1t=3\Rightarrow t + {1 \over t} = 3

⇒\Rightarrow The number of real roots = 2

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring