The maximum number of zeros of $p(x) = ax^4 + bx^3 + cx^2 + dx + e$ where $a \neq 0$ and $a, b, c, d, e \in R$ can be:

Obtain a quadratic polynomial with the following conditions:
The sum of the zeros $= \frac{1}{4}$;
The product of the zeros $= -1$.

From the following figure,find the number of zeros of $y=p(x)$ :

If the product of the zeros of $p(x) = ax^{2} - 6x - 6$ is $4$,then $a = $ ............

If the zeros of the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ $(a \neq 0)$ are $\alpha, \beta,$ and $\gamma,$ then $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} = \dots$

Find the division of the following by synthetic division method: $p(x) = x^{4} - a^{4}$ by $x - a$.