Obtain the zeros of $p(x) = 6x^2 - x - 2$. Also,verify the relationship between the zeros and the coefficients of $p(x)$.

The zero of the linear polynomial $p(x) = ax + b$ is $\ldots \ldots \ldots \ldots$ $(a, b \neq 0)$.

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 $\alpha^2 \beta \gamma + \alpha \beta^2 \gamma + \alpha \beta \gamma^2 = \dots$

If the polynomial $p(x) = x^{3} - 3x^{2} + x + 2$ is divided by the divisor polynomial $s(x)$, then the quotient polynomial $q(x) = x - 2$ and the remainder polynomial $r(x) = -2x + 4$ are obtained. Find the divisor polynomial $s(x)$.

Identify the type of the following polynomial based on its degree: $p(x) = (x - 15)(x + 15)$

The zeroes of the quadratic polynomial $x^{2}+99x+127$ are