Find number of real roots of equation $$e^{4x} + e^{3x} – 4e^{2x} + e^{x} + 1 = 0$$ is
what i try
$$\frac{e^{4x}+e^{3x}+e^x+1}{4}\geq \bigg(e^{4x}\cdot e^{3x}\cdot e^x\cdot 1\bigg)^{\frac{1}{4}}$$
$$e^{4x}+e^{3x}+e^{x}+1\geq 4e^{2x}$$
equality hold when $e^{4x}=e^{3x}=e^{x}=1.$
How do i solve it Without Inequality
