If $a+b+c=1, a b+b c+c a=2$ and $a b c=3$, then the value of $a^{4}+b^{4}+c^{4}$ is equal to $....$

The number of distinct real roots of the equation $|\mathrm{x}||\mathrm{x}+2|-5|\mathrm{x}+1|-1=0$ is....................

The sum of the roots of the equation $x+1-2 \log _{2}\left(3+2^{x}\right)+2 \log _{4}\left(10-2^{-x}\right)=0$, is :

Let $\alpha$ and $\beta$ be two real numbers such that $\alpha+\beta=1$ and $\alpha \beta=-1 .$ Let $p _{ n }=(\alpha)^{ n }+(\beta)^{ n },p _{ n -1}=11$ and $p _{ n +1}=29$ for some integer $n \geq 1 .$ Then, the value of $p _{ n }^{2}$ is .... .

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

The number of real roots of the polynomial equation $x^4-x^2+2 x-1=0$ is