The number of real solutions of the equation $x|x+5|+2|x+7|-2=0$ is .....................

Solve $\sqrt{5} x^{2} + x + \sqrt{5} = 0$.

Let $f(x) = ax^{2} + bx + c$ be such that $f(1) = 3$,$f(-2) = \lambda$,and $f(3) = 4$. If $f(0) + f(1) + f(-2) + f(3) = 14$,then $\lambda$ is equal to...

If the set of all $a \in R$,for which the equation $2x^2 + (a-5)x + (15-3a) = 0$ has no real root,is the interval $(\alpha, \beta)$,and $X = \{x \in Z : \alpha < x < \beta\}$,then $\sum_{x \in X} x^2$ is equal to

The polynomial equation of degree $5$ whose roots are the roots of the equation $x^5-3x^4-x^3+11x^2-12x+4=0$ each increased by $2$,is

The sum of the fourth powers of the roots of the equation $16x^2-10x+1=0$ is