The number of real roots of the equation $x | x |-5| x +2|+6=0$, is

If $\alpha, \beta $ and $\gamma$ are the roots of equation ${x^3} - 3{x^2} + x + 5 = 0$ then $y = \sum {\alpha ^2} + \alpha \beta \gamma $ satisfies the equation

What is the sum of all natural numbers $n$ such that the product of the digits of $n$ (in base $10$ ) is equal to $n^2-10 n-36 ?$

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

Let $\mathrm{a}=\max _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}$ and $\beta=\min _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}$

If $8 x^{2}+b x+c=0$ is a quadratic equation whose roots are $\alpha^{1 / 5}$ and $\beta^{1 / 5}$, then the value of $c-b$ is equal to:

If $\alpha , \beta $ are the roots of the equation $x^2 - 2x + 4 = 0$ , then the value of $\alpha ^n +\beta ^n$ is