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Find a quadratic polynomial whose sum and product of zeroes are $0$ and $- 9$, respectively. Also, find the zeroes of the polynomial so obtained.
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Solution: Polynomial is $x^2 - 0 (x) + (- 9) = x^2 - 9$
For zeroes :
$x^2 - 9 = (x + 3) (x - 3)$
Zeroes are $- 3, 3$
For zeroes :
$x^2 - 9 = (x + 3) (x - 3)$
Zeroes are $- 3, 3$