This document contains 3 quadratic equations and discusses using the sum and product of roots to find an equation with given roots. It provides 3 examples: 1) an equation with roots x = 3 - 2i and x = 3 + 2i whose sum is 6 and product is -12, 2) an equation with roots -3 and 5 whose sum is 2 and product is -15, and 3) finding the other root is -4 given one root is 4.

1. Equation Roots Sum of Roots Product of Roots
x2 + 5x ­ 6 = 0
x2 ­ 2x ­ 24 = 0
2x2 ­ 7x ­ 15 = 0
1

2. It would be complicated to use the reverse foil method to find a
quadratic equation for imaginary roots.
Instead we will use the sum and product of the roots to figure it
out.
x = 3 ­ 2i and x = 3 + 2i
Sum of the roots:
Product of the roots:
2

3. Find a quadratic equation that has the roots
and
3

4. Suppose one root of the equation
is 4. Find the other root.
4