Intermediate Algebra (11th edition)

OBJECTIVE 5 Solve quadratic equations with solutions that are not real

numbers.In if there will be two nonreal complex solutions.

Solving for Nonreal Complex Solutions

Solve each equation.

(a)

or Square root property

or

The solution set is , or

(b)

or Square root property

or

or Add

The solution set is , or

(c)

Subtract 7.

Add 1 to each side.

Factor on the left. Add on the right.

or Square root property

or

or Add.

The solution set is E- 1 +i 26 , - 1 - i 26 F, or E- 1 i 26 F. NOW TRY

x=- 1 +i 26 x=- 1 - i 26 - 1

x+ 1 =i 26 x+ 1 =-i 26 2 - 1 =i

x+ 1 = 2 - 6 x+ 1 =- 2 - 6

1 x+ 122 =- 6

x^2 + 2 x+ 1 =- 7 + 1 C 211 22 D^2 =1;

x^2 + 2 x=- 7

x^2 + 2 x+ 7 = 0

5 - 2 + 4 i, - 2 - 4 i 6 5 - 2  4 i 6.

x=- 2 + 4 i x=- 2 - 4 i -2.

x+ 2 = 4 i x+ 2 =- 4 i 2 - 16 = 4 i

x+ 2 = 2 - 16 x+ 2 =- 2 - 16

1 x+ 222 =- 16

Ei 215 , -i 215 F Ei 215 F.

x=i 215 x=-i 215 2 - 1 =i

x= 2 - 15 x=- 2 - 15

x^2 =- 15

EXAMPLE 9

x^2 = k, k 6 0,

502 CHAPTER 9 Quadratic Equations, Inequalities, and Functions

NOW TRY
EXERCISE 9
Solve each equation.

(a)

(b)

(c)x^2 + 8 x+ 21 = 0

1 x+ 422 =- 36

t^2 =- 24

NOW TRY ANSWERS

9. (a)

(b)

(c)E- 4 i 25 F

5 - 4  6 i 6

E 2 i 26 F

Complete solution available
on the Video Resources on DVD

1.Concept Check Which of the following are quadratic equations?

A. B. C. D.

2.Concept Check Which quadratic equation identified in Exercise 1is in standard form?

3.Concept Check A student incorrectly solved the equation as follows.

WHAT WENT WRONG?

Factor.

or Zero-factor property

or Solve each equation.

4.Concept Check A student was asked to solve the quadratic equation and did

not get full credit for the solution set 546. WHAT WENT WRONG?

x^2 = 16

x= 7 x= 4

x- 2 = 5 x + 1 = 5

1 x- 221 x+ 12 = 5

x^2 - x- 2 = 5

x^2 - x- 2 = 5

x+ 2 y= 0 x^2 - 8 x+ 16 = 0 2 t^2 - 5 t= 3 x^3 +x^2 + 4 = 0

9.1 EXERCISES