1. Lesson 8-4: Solutions of Quadratics Objectives Students will: Determine the nature of solutions of a quadratic equation Find and use sums and products of solutions of quadratic equations Find a quadratic equation given its solutions

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

3. Nature of Solutions Determined by discriminant: b 2 – 4ac 3 possibilities: 1) b 2 – 4ac = 0 ; exactly 1 real solution 2) b 2 – 4ac > 0 ; 2 real # solutions 3) b 2 – 4ac < 0 ; 2 complex (have i) solutions that are conjugates Determine the type of solutions: Example 1Example 2 8x 2 + 9x + 1 = 04x 2 – 12x + 9 = 0 Example 3 6x 2 + 2x + 5 = 0

4. Sum and Product of Solutions Sum of solutionsProduct of solutions Sum of solutions = Product of solutions =

5. Example 4 Find the sum & product of solutions of 4x 2 – 3x + 2 = 0

6. Writing Equations – 2 ways: Sum/Product Roots x 2 – (sum)x + (product) = 0(x – r 1 )(x – r 2 ) = 0 Example 5 Write a quad. equation with a sumof solutions of -2 and product of 6

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

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