The sum and product of the zeroes of a quadratic polynomial are - $1 / 2$ and $- 3$ receptively. What is the quadratic polynomial?

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Solution

If a quadratic polynomial is of the form:
$a x^{2} + b x + c = 0$ $(a \neq 0)$
Then, sum of roots = $- b / a$ and product of roots = $c / a$
Therefore required quadratic:
$a x^{2} + b x + c = a (x^{2} + (b / a) x + (c / a))$
$= a (x^{2} + \frac{1}{2} x - 3)$ ( $a \neq 0$ )
Note: A unique polynomial is not possible.

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