The number of the real roots of the equation $(x+1)^{2}+|x-5|=\frac{27}{4}$ is ....... .

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

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..........

Let $S=\left\{ x : x \in R \text { and }(\sqrt{3}+\sqrt{2})^{ x ^2-4}+(\sqrt{3}-\sqrt{2})^{ x ^2-4}=10\right\} \text {. }$ Then $n ( S )$ is equal to

The sum of all non-integer roots of the equation $x^5-6 x^4+11 x^3-5 x^2-3 x+2=0$ is