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

If ${x^2} + px + 1$ is a factor of the expression $a{x^3} + bx + c$, then

Product of real roots of the equation ${t^2}{x^2} + |x| + \,9 = 0$

Let $\mathrm{x}_1, \mathrm{x}_2, \mathrm{x}_3, \mathrm{x}_4$ be the solution of the equation $4 x^4+8 x^3-17 x^2-12 x+9=0$ and $\left(4+x_1^2\right)\left(4+x_2^2\right)\left(4+x_3^2\right)\left(4+x_4^2\right)=\frac{125}{16} m$. Then the value of $\mathrm{m}$ is..........

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