If one factor of $x^{3}+4 x^{2}+8 x+a$ is $(x+2)$,then find the value of $a$.

The zeros of $p(x) = 3x^2 - x - 4$ are $\alpha$ and $\beta$,then $\alpha^2 \beta + \alpha \beta^2 = \ldots$

Find the number of real zeros of the following polynomial: $p(x) = x^{3} - 9x$.

If $a=1, \,b=-2 \sqrt{3}, \,c=2,$ then the standard quadratic polynomial is ..........

If $\alpha, \beta$,and $\gamma$ are the zeros of the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ where $a \neq 0$,then the product of its zeros $(\alpha \beta \gamma)$ is:

Find the zeroes of the polynomial $x^{2}+\frac{1}{6} x-2,$ and verify the relation between the coefficients and the zeroes of the polynomial.