6.3 solve quadratic equations by factoring

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6.3 solve quadratic equations by factoring

  1. 1. Solving Quadratic Equations …by Factoring
  2. 2. Solving Quadratic Equations by Factoring <ul><li>Get ZERO on one side by itself. </li></ul><ul><li>Factor. Consider Common Factors FIRST! </li></ul><ul><li>Set each factor = 0. </li></ul><ul><li>Solve each part. </li></ul>
  3. 3. Example 3-1a Answer: The solution set is {0 , –4}. Solve by factoring. Original equation Add 4 x to each side. Factor the binomial. Solve the second equation. Zero Product Property or
  4. 4. Example 3-1a Check Substitute 0 and –4 in for x in the original equation.
  5. 5. Example 3-1a Solve by factoring. Original equation Subtract 5 x and 2 from each side. Factor the trinomial. Zero Product Property or Solve each equation. Answer: The solution set is Check each solution.
  6. 6. Example 3-1b Answer: {0 , 3} Solve each equation by factoring. a. b. Answer:
  7. 7. Example 3-2a Answer: The solution set is {3}. Solve by factoring. Original equation Add 9 to each side. Factor. Zero Product Property or Solve each equation.
  8. 8. Example 3-2a Check The graph of the related function, intersects the x -axis only once. Since the zero of the function is 3 , the solution of the related equation is 3 .
  9. 9. Example 3-2b Answer: {–5} Solve by factoring.
  10. 10. Example 3-3a Read the Test Item You are asked to find the positive solution of the given quadratic equation. This implies that the equation also has a solution that is not positive. Since a quadratic equation can either have one, two, or no solutions, we should expect this equation to have two solutions. Multiple-Choice Test Item What is the positive solution of the equation ? A –3 B 5 C 6 D 7
  11. 11. Example 3-3a Solve the Test Item Answer: D Both solutions, –3 and 7 , are listed among the answer choices. However, the question asks for the positive solution, 7 . Original equation Factor. Divide each side by 2 . Factor. or Zero Product Property Solve each equation.
  12. 12. Example 3-3b Answer: C Multiple-Choice Test Item What is the positive solution of the equation ? A 5 B – 5 C 2 D 6
  13. 13. Example 3-4a Write a quadratic equation with and 6 as its roots. Write the equation in the form where a , b , and c are integers. Write the pattern. Simplify. Replace p with and q with 6 .
  14. 14. Example 3-4a Use FOIL. Multiply each side by 3 so that b is an integer. Answer: A quadratic equation with roots and 6 and integral coefficients is You can check this result by graphing the related function.
  15. 15. Example 3-4b Write a quadratic equation with and 5 as its roots. Write the equation in the form where a , b , and c are integers. Answer:

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