The sum of all the real roots of the equation $\left( e ^{2 x }-4\right)\left(6 e ^{2 x }-5 e ^{ x }+1\right)=0$ is
$\log _{ c } 3$
$-\log _{e} 3$
$\log _{ e } 6$
$-\log _{e} 6$
The number of real roots of the equation $\mathrm{e}^{4 \mathrm{x}}-\mathrm{e}^{3 \mathrm{x}}-4 \mathrm{e}^{2 \mathrm{x}}-\mathrm{e}^{\mathrm{x}}+1=0$ is equal to $.....$
The number of solutions, of the equation $\mathrm{e}^{\sin x}-2 e^{-\sin x}=2$ is
Consider the cubic equation $x^3+c x^2+b x+c=0$ where $a, b, c$ are real numbers. Which of the following statements is correct?
If the product of roots of the equation ${x^2} - 3kx + 2{e^{2\log k}} - 1 = 0$ is $7$, then its roots will real when
The sum of all the roots of the equation $\left|x^2-8 x+15\right|-2 x+7=0$ is: