The graph of $p(x) = -x^2 + x + 6$ is a.........

Are the following statements 'True' or 'False'? Justify your answers.
If the zeroes of a quadratic polynomial $ax^2 + bx + c$ are both positive,then $a, b$ and $c$ all have the same sign.

Find the zeros of the cubic polynomial $p(x)=4 x^{3}+10 x^{2}+6 x$ and also verify the relationship between the zeros and the coefficients.

The product of the zeros of $p(x) = 4x^{2} + 12x + 5$ is..........

The product of zeros of a cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ is $\ldots \ldots \ldots$

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