A26-7 Fundamental Thm of Algebra

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A26-7 Fundamental Thm of Algebra

  1. 1. Fundamental Theorem of Algebra Algebra 2 6.7 p. 366
  2. 2. Fundamental Theorem of Algebra <ul><li>If f ( x ) is a polynomial of degree n > 0, then the equation f ( x ) = 0 has at least one root in the set of complex numbers. </li></ul>
  3. 3. Fundamental Theorem of Algebra <ul><li>If you count all the real , imaginary , and repeated solutions, an n th-degree polynomial has exactly n solutions. </li></ul>
  4. 4. Solutions <ul><li>Solutions are also called “roots” or “zeros” </li></ul>
  5. 5. Solutions <ul><li>All real zeros of a function are x-intercepts . </li></ul>
  6. 6. Solutions <ul><li>All real zeros of a function are x-intercepts . </li></ul><ul><li>Repeated zeros only touch the x-axis. </li></ul>
  7. 7. Solutions <ul><li>All real zeros of a function are x-intercepts . </li></ul><ul><li>Repeated zeros only touch the x-axis. </li></ul><ul><li>Non-repeated zeros cross the x-axis. </li></ul>
  8. 8. Solutions <ul><li>All real zeros of a function are x-intercepts . </li></ul><ul><li>Repeated zeros only touch the x-axis. </li></ul><ul><li>Non-repeated zeros cross the x-axis. </li></ul><ul><li>Complex roots occur in conjugates . </li></ul>

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