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anonymous

  • 4 years ago

Describe how you would analyze the zeros of the polynomial function f(x) = -3x5 - 8x4 +25x3 - 8x2 +x - 19 using Descartes' Rule of Signs and include the answer.

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  1. amistre64
    • 4 years ago
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    the Drule is to count sign (operation) changes for f(x) and f(-x)

  2. amistre64
    • 4 years ago
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    f(x) = -3x5 - 8x4 +25x3 - 8x2 +x - 19 1 | 1 | 1 | 1| 0 | 4 sign chagnes in f(x) there are: 4, 2 or 0 positive zeros

  3. amistre64
    • 4 years ago
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    f(-x) = 3x5 - 8x4 -25x3 - 8x2 -x - 19 1 | 0 | there is 1 sign change for f(-x); there is at least 1 negative zero

  4. amistre64
    • 4 years ago
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    since a zero can be a complex value; and complexes come in pairs; we count the real values down by 2s

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