Question

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

Answer 1

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