SOLUTION: 9x^5+9x^4+65x^3+65x^2-144x-144 what are the rational(zero) roots? I am unable to get the answer.

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Question 1000554: 9x^5+9x^4+65x^3+65x^2-144x-144
what are the rational(zero) roots? I am unable to get the answer.
Found 2 solutions by solver91311, MathLover1:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Use the Rational Roots Test. If a polynomial function has a rational zero, it will be of the form where is a factor of the constant term and is a factor of the lead coefficient.

Using the Rational Roots Test, create your list of possible zeros. Counting both positive and negative possibilities you have 39 possible rational zeros for your polynomial.

Then start testing them using Synthetic Division. I'll save you a little work: once you have found three real zeros, you have found them all. The other two zeros are complex.

If you need a refresher on Synthetic Division, look here:

Purple Math Synthetic Division

Note that there are 4 pages; read them all.

John

My calculator said it, I believe it, that settles it

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

9x%5E5%2B9x%5E4%2B65x%5E3%2B65x%5E2-144x-144=0....factor completely
%289x%5E5%2B9x%5E4%29%2B%2865x%5E3%2B65x%5E2%29-%28144x%2B144%29=0
9x%5E4%28x%2B1%29%2B65x%5E2%28x%2B1%29-144%28x%2B1%29=0
%289x%5E4%2B65x%5E2-144%29%28x%2B1%29=0
%289x%5E4%2B81x%5E2-16x%5E2-144%29%28x%2B1%29=0
%28%289x%5E4%2B81x%5E2%29-%2816x%5E2%2B144%29%29%28x%2B1%29=0
%289x%5E2%28x%5E2%2B9%29-16%28x%5E2%2B9%29%29%28x%2B1%29=0
%289x%5E2-16%29%28x%5E2%2B9%29%28x%2B1%29=0
%28%283x%29%5E2-4%5E2%29%28x%5E2%2B9%29%28x%2B1%29=0
%283x-4%29%283x%2B4%29%28x%5E2%2B9%29%28x%2B1%29=0
solutions:
if %283x-4%29=0=>3x=4=>highlight%28x=4%2F3%29
if %283x%2B4%29=0=>3x=-4=>highlight%28x=-4%2F3%29
if %28x%5E2%2B9%29=0=>x%5E2=-9=>x=sqrt%28-9%29=>highlight%28x=3i%29 and highlight%28x=-3i%29
if %28x%2B1%29=0=>highlight%28x=-1%29