The number of roots of the equation $\log ( - 2x)$ $ = 2\log (x + 1)$ are

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?

The number of solutions of the equation $x ^2+ y ^2= a ^2+ b ^2+ c ^2$. where $x , y , a , b , c$ are all prime numbers, is

The sum of all the solutions of the equation $(8)^{2 x}-16 \cdot(8)^x+48=0$ is :

$\{ x \in R:|x - 2|\,\, = {x^2}\} = $

If $\alpha , \beta$ and $\gamma$ are the roots of ${x^3} + 8 = 0$, then the equation whose roots are ${\alpha ^2},{\beta ^2}$ and  ${\gamma ^2}$ is