Obtain the quadratic polynomial in the standard form with the following coefficients: $a=1, b=-10, c=25$.

From the following figure,find the number of real zeros of $y=p(x)$:

Obtain a quadratic polynomial with the following conditions:
The sum of the zeros $= \frac{1}{4}$;
The product of the zeros $= -1$.

The graph of a linear polynomial $p(x) = ax + b$ intersects the $X$-axis at $\ldots \ldots \ldots \ldots$ (where $a \neq 0$).

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

If the remainder on division of $x^{3}+2 x^{2}+k x+3$ by $x-3$ is $21$,find the quotient and the value of $k$. Hence,find the zeroes of the cubic polynomial $x^{3}+2 x^{2}+k x-18$.