11 1 The Square Root Principle and Completing

11. 1 The Square Root Principle and Completing the Square 1. Use the square root principle to solve quadratic equations. 2. Solve quadratic equations by completing the square.

Solve: Quadratic Equation Set = 0 Two solutions

The Square Root Principle If , then Isolated perfect square. No middle term. Always 2 solutions. .

What do you see? Solve: Fractions Perfect square – no m term 3 5 1 1 4∙ 15

Solve. a) b) c) d) 11. 1 Copyright © 2011 Pearson Education, Inc. Slide 11 - 5

Solve. a) b) c) d) 11. 1 Copyright © 2011 Pearson Education, Inc. Slide 11 - 6

Solve:

Solve:

Solve: 4∙ 7

2 rational solutions 2 irrational solutions 2 non-real imaginary solutions

Solve. a) b) c) d) 11. 1 Copyright © 2011 Pearson Education, Inc. Slide 11 - 11

Solve. a) b) c) d) 11. 1 Copyright © 2011 Pearson Education, Inc. Slide 11 - 12

Completing the Square squared ½ Coefficient of the squared term must be 1. squared ½ squared + 3 + 9 ½ squared - 7 ½ + 49

Solve: Coefficient of squared term is 1. + 25 ½ + 5 + 25 squared 13 2 irrational solutions

Solve: Coefficient of squared term is NOT 1. 9 4 ½ 10 + 9 = 4 4 4 squared 3 2 2 irrational solutions

Solve: ½ Coefficient of squared term is NOT 1. squared 2 rational solutions Factorable!

Solve by completing the square. a) b) c) d) 11. 1 Copyright © 2011 Pearson Education, Inc. Slide 11 - 17

Solve by completing the square. a) b) c) d) 11. 1 Copyright © 2011 Pearson Education, Inc. Slide 11 - 18