how to write a quadratic if the product of the roots is -3?

We can write a quadratic equation with roots a and b
as:

(x - a)(x - b) =
0

=> x^2 - (a+b)x + ab =
0

as the product of the roots is
-3.

=> x^2 - ( a + b) - 3 =
0

Now a and b can have several values which satisfy the
condition that their product is -3, e.g. (-1 , 3) , ( 3/2 , -2) etc. We are not given
any further information about what the roots are.

Therefore
the quadratic equation is

x^2 - (a + b) - 3 =
0