The Product of the Roots of a Quadratic
To find the product of the roots of a quadratic in the form
ax^{ 2} + bx + c = 0, use the formula
product of roots
If the ax^{ 2} term is on the opposite side of the
constant term, use a negative (  c/a ).
Example:
Find the product of the roots of 4x^{ 2}  3x  12 =
0. Using the formula, a = 4 and c =  12, so the product is .
Proof:
Let the quadratic be ax^{ 2} + bx + c = 0 with roots r
and s . Then from the quadratic formula,
So,
