If the zero of the polynomial $p(x) = ax^2 - 11x + 3$ is $1$,then $a = \ldots$

The maximum number of zeros of a polynomial having degree $k+1$ can be........

State the degree of the following polynomial: $p(x) = (x^{1/2})^{50} - 5x^{10} - 9x^2 + 15$.

If the zeros of the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ ($a \neq 0$; $a, b, c, d \in R$) are $\alpha, \beta$,and $\gamma$,then $\alpha^2 \beta \gamma + \alpha \beta^2 \gamma + \alpha \beta \gamma^2 = \dots$

Factorize the following polynomial: $p(x) = x^{3} - 4x^{2} + 5x - 20$.

The zeros of cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$; $a \neq 0, a, b, c, d \in R$ are $\alpha, \beta$ and $\gamma$; then $\alpha\beta + \beta\gamma + \gamma\alpha = \ldots$