1. Section 8.3 The Discriminant and the Nature of Solutions  The Discriminant  Type and Number of Solutions  Writing Equations from Solutions 8.31

2. Introducing … The Discriminant!  is the Radicand Part of the Quadratic Equation  It predicts the types of solutions. If b 2 – 4ac is positive:two different real numbers 0:one real (two equal real numbers) negative:two different complex numbers positive perfect square: two different rational numbers positive but imperfect: two different irrational numbers 8.32

3. What Types of Solutions? b 2 – 4ac 8.33

4. Writing Equations from Solutions  We can use the reverse of the Principle of Zero Products  (x – 2)(x + 3) = 0 means solutions x = 2 and x= -3  Think: x 2 + x – 6 = 0 is equivalent to 2x 2 + 2x – 12 = 0 Many quadratic equations can have the same solutions  Find an equation having solutions: x = 3 and x = 5/2 x = ±2i x = ± x = 0, x = -4 and x = 1 8.34

5. What Next? Quadratic Applications  Section 8.4 Section 8.4 8.35