Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively: $4, 1$.

(A) Let the quadratic polynomial be $p(x) = ax^2 + bx + c$,where $\alpha$ and $\beta$ are its zeroes.
The sum of the zeroes is given by $\alpha + \beta = 4 = \frac{4}{1} = \frac{-b}{a}$.
The product of the zeroes is given by $\alpha \times \beta = 1 = \frac{1}{1} = \frac{c}{a}$.
By comparing the ratios,if we assume $a = 1$,then $b = -4$ and $c = 1$.
Substituting these values into the general form $ax^2 + bx + c$,we get the quadratic polynomial $x^2 - 4x + 1$.