1. Warm-up 8-4: ACT – Set 2 - #8, 9, 10
What part of the quadratic formula determines what kind of solutions you will get?

2. 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

3. 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 = x2 – 12x + 9 = 0
Example 3
6x2 + 2x + 5 = 0

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

5. Writing Equations – 2 ways: Sum/Product Roots
x2 – (sum)x + (product) = 0 (x – r1)(x – r2) = 0
Example 4 Example 5
Find the sum & product of solutions Write a quad. equation with a sum
of 4x2 – 3x + 2 = 0 of solutions of -2 and product of 6
Example 6
Write a quad. equation with solutions 5 and 7

6. HW 96