Question

Find a quadratic polynomial whose sum of zeroes is 0 and one zero is 5

Answer 1

Dear Student

You are doing right just put polynomial equals to 0 because $\alpha and\beta$ are zeroes of the polynomial.
k(x² - 25) = 0
x² - 25 = 0 is required polynomial

You can also check,
x=$\sqrt{25}$ = $\pm 5$ are zeros

Regards