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Find a quadratic polynomial, sum and product of whose zeroes are 5 and $- 6$, respectively. Also, find the zeroes of the polynomial so obtained.
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Solution: Required polynomial is $x^2 - 5x - 6$
For zeroes; $x^2 - 5x - 6 = (x - 6) (x + 1)$
Zeroes are $x = 6, - 1$
For zeroes; $x^2 - 5x - 6 = (x - 6) (x + 1)$
Zeroes are $x = 6, - 1$