1. Bell Ringer: Find the zeros of each function.4.
f(x) = x2 – 18x + 16 5.
f(x) = x2 + 8x – 24

2. Objectives Define and use imaginary and complex numbers.
Solve quadratic equations with complex roots.

3. Example 2A: Solving a Quadratic Equation with Imaginary Solutions
Solve the equation.
Take square roots.
Express in terms of i.
Check
x2 = –144
–144
(12i)2
144i 2
144(–1) 
x2 = –144
–144
144(–1)
144i 2
(–12i)2 

4. The discriminant is part of the Quadratic Formula that you can use to determine the number of real roots of a quadratic equation.

5. Make sure the equation is in standard form before you evaluate the discriminant, b2 – 4ac.
Caution!