Lesson 8-4: Solutions of Quadratics

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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

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What part of the quadratic formula determines
what kind of solutions you will get?
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Nature of Solutions Determined by discriminant
b2 4ac 3 possibilities 1) b2 4ac 0
exactly 1 real solution 2) b2 4ac gt
0 2 real solutions 3) b2 4ac lt 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
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Sum and Product of Solutions Sum of
solutions Product of solutions
Sum of solutions Product of solutions
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Example 4 Find the sum product of
solutions of 4x2 3x 2 0
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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
7

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

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Assignment

• 8-4/ 357 / 3-55 eoo 73-81o