Lesson 8-4: Solutions of Quadratics

ObjectivesStudents will:Determine the nature of solutions of a quadratic equationFind and use sums and products of solutions of quadratic equationsFind a quadratic equation given its solutions

What part of the quadratic formula determines what kind of solutions you will get?

a

acbbx

2

42

Nature of Solutions

Determined by discriminant: b2 – 4ac

3 possibilities:

1) b2 – 4ac = 0 ; exactly 1 real solution

2) b2 – 4ac > 0 ; 2 real # solutions

3) b2 – 4ac < 0 ; 2 complex (have i) solutions that are conjugates

Determine the type of solutions:

Example 1 Example 2

8x2 + 9x + 1 = 0 4x2 – 12x + 9 = 0

Example 3

6x2 + 2x + 5 = 0

Sum and Product of Solutions

Sum of solutions Product of solutions

a

acbb

2

42 a

acbb

2

42

a

acbb

2

42 a

acbb

2

42

Sum of solutions = Product of solutions =

a

ba

c

Example 4

Find the sum & product of solutions

of 4x2 – 3x + 2 = 0

Writing Equations – 2 ways:

Sum/Product Roots

x2 – (sum)x + (product) = 0 (x – r1)(x – r2) = 0

Example 5

Write a quad. equation with a sum of solutions of -2 and product of 6

• Example 6Write a quad. equation with solutions 5 and 7

Assignment

8-4/ 357 / 3-55 eoo 73-81o