Question

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.

Answer 1

the Drule is to count sign (operation) changes for f(x) and f(-x)

Answer 2

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

Answer 3

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

Answer 4

since a zero can be a complex value; and complexes come in pairs; we count the real values down by 2s