Find the zeros of the following quadratic polynomial: $p(x) = x^{2} + x - 12$.

Obtain a quadratic polynomial $p(x) = ax^2 + bx + c$,where the sum of zeros is $\sqrt{2}$ and the product of zeros is $\frac{1}{3}$,given that $a < 0$.

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

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

The coefficient of the underlined term of $p(x) = 7 - \underline{5x^4} - 2x^3 - x^2$ is $\ldots \ldots$

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.