The number of real roots of the equation $5 + |2^x - 1| = 2^x(2^x - 2)$ is
$4$
$3$
$2$
$1$
lf $2 + 3i$ is one of the roots of the equation $2x^3 -9x^2 + kx- 13 = 0,$ $k \in R,$ then the real root of this equation
The number of ordered pairs $(x, y)$ of real numbers that satisfy the simultaneous equations $x+y^2=x^2+y=12$ is
The product of the roots of the equation $9 x^{2}-18|x|+5=0,$ is
The sum of integral values of $a$ such that the equation $||x\ -2|\ -|3\ -x||\ =\ 2\ -a$ has a solution
The number of integers $n$ for which $3 x^3-25 x+n=0$ has three real roots is