If an angle $A$ of a $\Delta ABC$ satisfies $5 \cos A + 3 = 0$,then the roots of the quadratic equation $9x^2 + 27x + 20 = 0$ are

The number of ordered pairs $(x, y)$ of integers satisfying $x^3+y^3=65$ is

If the roots of $\sqrt{\frac{1-y}{y}}+\sqrt{\frac{y}{1-y}}=\frac{5}{2}$ are $\alpha$ and $\beta$ $(\beta > \alpha)$ and the equation $(\alpha+\beta) x^4-25 \alpha \beta x^2+(\gamma+\beta-\alpha)=0$ has real roots,then a possible value of $\gamma$ is

If $x^2+p x+1$ is a factor of $a x^3+b x+c$,then

Let $S = \{x \in [-6, 3] \setminus \{-2, 2\} : \frac{|x+3|-1}{|x|-2} \geq 0\}$ and $T = \{x \in \mathbb{Z} : x^2 - 7|x| + 9 \leq 0\}$. Then the number of elements in $S \cap T$ is $....$

If $\alpha$ and $\beta$ are the roots of the equation $ax^2 + bx + c = 0$,and $\alpha + \beta$,$\alpha^2 + \beta^2$,and $\alpha^3 + \beta^3$ are in a geometric progression,and $\Delta = b^2 - 4ac$,then which of the following is true?