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

Find the zeros of the quadratic polynomial $p(x) = 10x^2 - 14x - 12$ and also find the sum and the product of the zeros of the polynomial.

Given that the zeroes of the cubic polynomial $x^{3}-6x^{2}+3x+10$ are of the form $a, a+b, a+2b$ for some real numbers $a$ and $b$,find the values of $a$ and $b$ as well as the zeroes of the given polynomial.

State the degree of the following polynomial: $p(x) = 5x^8 - 6(x^2)^5 - 4x^3 - 14$.

The zero of $p(x) = -x^2 + 2x - 1$ is..........

The zeros of the quadratic polynomial $p(x) = x^{2} - 3x + 2$ are $\alpha$ and $\beta$. Then,$\frac{1}{\alpha} + \frac{1}{\beta} = \ldots$