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

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