Question

Using complete sentences, describe how you would find all possible rational zeros of the polynomial function f(x) = 9x4 – 17x3 + 2x2 – 3x + 33.

Be sure to provide the answer in your explanation.

Answer 1

http://www.mathwords.com/r/rational_root_theorem.htm

Answer 2

then again, let me add a few more things, the leading term of this polynomial is a 9x^4, so this polynomial doesn't even have to have rational zeros, which would make that problem much more tricky.

Answer 3

it is shifted up by +33 units, so the thought is near that it doesn't intersect with the x-axis.

Answer 4

oh ok

Answer 5

if the leading term would have been -17x^3 we would know that there must be at least one non-complex root. But in this case, however, there are no rational zeros.

Answer 6

How could I destribe how to get the rational zeros

Answer 7

The rational zeros are, [plus or minus] +-(1,3,11,33,1/3,11/3,1/9,11/9) is that correct

Answer 8

yes, that seems right to me at first glance, quite an exhaustive problem as you see (-: So, in fact, you have to plot them in now to see if one of them works, if not, then your answer is that there are no rational roots.