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

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

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 Sum of solutions = Product of solutions =

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

HW 96