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Lesson 6.5: The Quadratic Formula and the Discriminant, pg. 313

Lesson 6.5: The Quadratic Formula and the Discriminant, pg. 313. Goals: To solve quadratic equations by using the Quadratic Formula. To use the discriminant to determine the number and type of roots of a quadratic equation. Quadratic Formula.

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Lesson 6.5: The Quadratic Formula and the Discriminant, pg. 313

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  1. Lesson 6.5: The Quadratic Formula and the Discriminant, pg. 313 Goals: To solve quadratic equations by using the Quadratic Formula. To use the discriminant to determine the number and type of roots of a quadratic equation.

  2. Quadratic Formula • The solutions of a quadratic equation of the form ax² + bx + c = 0, where a ≠ 0, are given by the following formula. • To solve quadratic equations using the quadratic formula, the equation must be set equal to ZERO

  3. Example 1: Solve by using the quadratic formula. 1. x² - 8x = 33

  4. 2. x² - 34x + 289 = 0

  5. 3. x² - 6x + 2 = 0

  6. 4. x² + 13 = 6x

  7. Discriminant:To find the number and types of roots of a quadratic equation use b² - 4ac b² - 4ac > 0; 2 real rational roots b² - 4ac is perfect square b² - 4ac > 0; 2 real irrational roots b² - 4ac is not a perfect square b² - 4ac = 0; 1 real rational root b² - 4ac < 0; 2 complex roots

  8. 1. x² + 6x + 9 = 0 2. x² + 3x + 5 = 0 Ex. 2: Describe the roots using the discriminant.

  9. 3. x² + 8x – 4 = 0 4. x² - 11x + 10 = 0

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