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4.6 Quadratic formula

Learn how to solve quadratic equations using the quadratic formula with examples showcasing rational, irrational, and complex roots. Understand discriminants and types of roots. Find solutions and values for various equations.

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4.6 Quadratic formula

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  1. 4.6 Quadratic formula

  2. Concept

  3. x2 – 8x = 33 1x2 – 8x – 33 = 0 Example 1 Two Rational Roots Solve x2 – 8x = 33 by using the Quadratic Formula. First, write the equation in the form ax2 + bx + c = 0 and identify a, b, and c. Then, substitute these values into the Quadratic Formula. Quadratic Formula

  4. Solve x2 + 13x = 30 by using the Quadratic Formula.

  5. Example 2 One Rational Root Solve x2 – 34x + 289 = 0 by using the Quadratic Formula.

  6. Example 3 Irrational Roots Solve x2 – 6x + 2 = 0 by using the Quadratic Formula.

  7. Example 4 Complex Roots Solve x2 + 13 = 6x by using the Quadratic Formula.

  8. Solve x2 + 5 = 4x by using the Quadratic Formula.

  9. Concept

  10. Example 5 Describe Roots A.Findthevalueofthediscriminantforx2+3x + 5 = 0. Then describe the number and type of roots for the equation.

  11. Example 5 Describe Roots B.Findthevalue of the discriminant forx2–11x+ 10 = 0. Then describe the number and type of roots for the equation.

  12. Give the values of b for which the equation has two real solutions • 3x2 + bx + 27=0

  13. Concept

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