The number of real roots of the equation $5 + |2^x - 1| = 2^x(2^x - 2)$ is
$4$
$3$
$2$
$1$
If $\alpha, \beta$ are the roots of the equation, $x^2-x-1=0$ and $S_n=2023 \alpha^n+2024 \beta^n$, then
The locus of the point $P=(a, b)$ where $a, b$ are real numbers such that the roots of $x^3+a x^2+b x+a=0$ are in arithmetic progression is
If $x$ be real, then the maximum value of $5 + 4x - 4{x^2}$ will be equal to
The number of roots of the equation $|x{|^2} - 7|x| + 12 = 0$ is
The sum of all the solutions of the equation $(8)^{2 x}-16 \cdot(8)^x+48=0$ is :