Question

What are the possible number of positive, negative, and complex zeros of f(x) = 3x4 – 5x3 – x2 – 8x + 4 ?
Answer
Positive: 2; Negative: 2; Complex: 4 or 2 or 0
Positive: 3 or 1; Negative: 1; Complex: 2 or 0
Positive: 1; Negative: 3 or 1; Complex: 2 or 0
Positive: 2 or 0; Negative: 2 or 0; Complex: 4 or 2 or 0

Answer 1

im guessing the last one ....

Answer 2

2 sign changes in + gives us either 2 or 0 roots

Answer 3

product of roots is +4, so positive 0 or 2, neghative 2 or 0. Complex roots always in pairs, so 0, 2 or 4 are the complex possibilities, so yes amistre64 is correct

Answer 4

Ooops! Why not 4 positives or 4 negatives?

Answer 5

4 positives not possible because some of the coefficients are negative

Answer 6

4 negatives not possible because sum of roots =-(-5)

Answer 7

Here are some general theorems about polynomials which might come in handy: http://home.windstream.net/okrebs/page26.html