Pre-Calculus Lesson 5: Solving Quadratic EquationsFactoring, quadratic formula, and discriminant

Steps to Follow

1. Set the equation equal to zero.

2. Factor.3. Set each factor equal to

zero (set up a T-chart).4. Solve.

036132 xx

036132 xx 049 xx

036132 xx 049 xx

09 x 04 x

9x 4x

1032 xx

1032 xx01032 xx

1032 xx01032 xx

025 xx

1032 xx01032 xx

025 xx

05 x 02 x

5x 2x

103 2 xx

103 2 xx0103 2 xx

103 2 xx0103 2 xx

0253 xx

103 2 xx0103 2 xx

0253 xx

053 x 02 x

3

5x 2x

032 2 xx

032 2 xx 0132 xx

032 2 xx 0132 xx

032 x 01 x

2

3x 1x

Quadratic Formula

a

acbbx

2

42

0153 2 xx

a

acbbx

2

42

a

acbbx

2

42

32

13455 2 x

0153 2 xx

a

acbbx

2

42

32

13455 2 x

6

12255 x

0153 2 xx

a

acbbx

2

42

32

13455 2 x

6

12255 x

6

135x

0153 2 xx

935 2 xx

0935 2 xx935 2 xx

a

acbbx

2

42

935 2 xx0935 2 xx

a

acbbx

2

42

52

95433 2 x

935 2 xx0935 2 xx

a

acbbx

2

42

52

95433 2 x

10

18093 x

935 2 xx0935 2 xx

a

acbbx

2

42

52

95433 2 x

10

18093 x

10

1893x

935 2 xx0935 2 xx

012 xx

a

acbbx

2

42

a

acbbx

2

42

12

11411 2 x

012 xx

a

acbbx

2

42

12

11411 2 x

2

411 x

012 xx

a

acbbx

2

42

12

11411 2 x

2

411 x

2

31 x

012 xx

a

acbbx

2

42

12

11411 2 x

2

411 x

2

31 x

2

31 i

012 xx

Discriminant What is the formula for the discriminant?

What does the discriminant tell us about roots?

◦ If positive?

◦ If =0?

◦ If negative?

Discriminant What is the formula for the discriminant?

What does the discriminant tell us about roots?

◦ If positive?

◦ If =0?

◦ If negative?

acb 42

Discriminant What is the formula for the discriminant?

What does the discriminant tell us about roots?

◦ If positive?

◦ If =0?

◦ If negative?

acb 42

2 real roots

Discriminant What is the formula for the discriminant?

What does the discriminant tell us about roots?

◦ If positive?

◦ If =0?

◦ If negative?

acb 42

2 real roots

1 real root

Discriminant What is the formula for the discriminant?

What does the discriminant tell us about roots?

◦ If positive?

◦ If =0?

◦ If negative?

acb 42

2 real roots

1 real root

2 imaginary roots0 real roots

0142 xx

acb 42

0142 xx

acb 42 11442

0142 xx

acb 42 11442

12416

0142 xx

acb 42 11442

12416

2 real roots

723 2 xx

723 2 xx

0723 2 xx

723 2 xx

acb 42

0723 2 xx

723 2 xx

acb 42

0723 2 xx

73422

723 2 xx

acb 42

80844

0723 2 xx

73422

723 2 xx

acb 42

80844

0 real roots2 imaginary roots

0723 2 xx

73422