Question

The number of real roots of the equation $e^{4x}+2e^{3x}-e^x-6=0$ is :

• A. 2
• B. 4
• C. 1
• D. 0

Answer 1

Answer: (C)

Let $e^x=t>0$
$f(t)=t^4+2t^3-t-6=0$
$f^{\prime }(t)=4t^3+6t^2-1$

$f^{\prime \prime }(t)=12t^2+12t>0$

$f(0)=-6,f(1)=-4,f(2)=24$
$\Rightarrow$ Number of real roots $=1$