Holt McDougal Algebra 2

2-5 Complex Numbers and Roots

4.

5.

f(x) = x2 – 18x + 16

f(x) = x2 + 8x – 24

Bell Ringer: Find the zeros of each function.

Holt McDougal Algebra 2

2-5 Complex Numbers and Roots

Define and use imaginary and complex numbers.

Solve quadratic equations with complex roots.

Objectives

Holt McDougal Algebra 2

2-5 Complex Numbers and Roots

Solve the equation.

Example 2A: Solving a Quadratic Equation with Imaginary Solutions

Take square roots.

Express in terms of i.

Checkx2 = –144

–144–144–144

(12i)2

144i 2

144(–1)

x2 = –144

–144–144–144144(–1)

144i 2

(–12i)2

Holt McDougal Algebra 2

2-5 Complex Numbers and Roots

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

Holt McDougal Algebra 2

2-5 Complex Numbers and Roots

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

Caution!