The solution of the equation $2x^2 + 3x - 9 \le 0$ is given by

The sum of the fourth powers of the roots of the equation $x^3+x+1=0$ is

The set of all values of $k$ for which the inequality $x^2 - (3k + 1)x + 4k^2 + 3k - 3 > 0$ is true for all real values of $x$ is

Let $S$ be the set of positive integral values of $a$ for which $\frac{ax^2+2(a+1)x+9a+4}{x^2-8x+32} < 0, \forall x \in R$. Then,the number of elements in $S$ is:

Statement $(I)$: The set of solutions of $|x|^2 - 4|x| + 3 < 0$ is the interval $(-3, 3)$.
Statement $(II)$: If $x < 3$ or $x > 5$, then $x^2 - 8x + 15 > 0$.
Which of the above statements is (are) true?

If $\alpha_1, \alpha_2$ and $\alpha_3$ are the roots of $x^3+3x+2=0$,then $\alpha_1^5+\alpha_2^5+\alpha_3^5=$