If two roots of the equation ${x^3} - 3x + 2 = 0$ are same, then the roots will be

The sum of the cubes of all the roots of the equation $x^{4}-3 x^{3}-2 x^{2}+3 x+1=10$ is

Let $\alpha$ and $\beta$ be the roots of $x^2-6 x-2=0$, with $\alpha>\beta$. If $a_n=\alpha^n-\beta^n$ for $n \geq 1$, then the value of $\frac{a_{10}-2 a_8}{2 a_9}$ is

The number of roots of the equation $|x{|^2} - 7|x| + 12 = 0$ is

The set of all real numbers $x$ for which ${x^2} - |x + 2| + x > 0,$ is

The number of real solutions of the equation $|{x^2} + 4x + 3| + 2x + 5 = 0 $are