Let $\mathrm{S}=\left\{x^3+a x^2+b x+c: a, b, c \in \mathrm{~N}\right.$ and $\left.a, b, c \leq 20\right\}$ be a set of polynomials. Then the number of polynomials in S , which are divisible by $x^2+2$, is

The smallest positive integral value of $a$, for which all the roots of $x^4-a x^2+9=0$ are real and distinct, is equal to

The number of the real solutions of the equation: $x|x+3|+|x-1|-2=0$ is

If the domain of the function

$$ f(x)=\log _{\left(10 x^2-17 x+7\right)}\left(18 x^2-11 x+1\right) $$

is $(-\infty, a) \cup(b, c) \cup(d, \infty)-\{e\}$, then

$90(a+b+c+d+e)$ equals: