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

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

The zeros of $p(x) = x^{2} + 4x + 3$ are.........

For the zeros $\alpha$ and $\beta$ of the polynomial $p(x) = ax^2 + bx + c$,what is the value of $\frac{1}{\alpha} + \frac{1}{\beta}$?

Prove that $-6, -\frac{1}{2}$ and $1$ are the zeros of the cubic polynomial $p(x) = 2x^3 + 11x^2 - 7x - 6$. Also,verify the relationship between the zeros and the coefficients.

If one zero of the quadratic polynomial $x^{2}+3x+k$ is $2$,then the value of $k$ is