You are here:

Advanced Math/Find all the rational zeros...

Advertisement

Expert: - 6/27/2005


Question
   Find all the rational zeros of g(x) = 2x^3 - 11x^2 + 8x + 21.  

Answer
Using the rational roots theorem, you check every possible factor of 21 divided by every possible factor of 2 , so you go through the list
{ +-21, +-21/2, +-7, +-7/2, +-3, +-3/2, +-1, +-1/2 }

and look for zeros. Actually, it is easy to check the whole numbers first, and find x=-1 is a zero. Then divide the polynomial by x+1 and get
2x^2 - 13x + 21 = (2x-7)(x-3).
So the other zeros are x=3 and x=7/2, and you see they appear in the list above.
The answer is {-1, 3 , 7/2}

Advanced Math

All Answers

Answers by Expert:

Ask Experts

Volunteer

Socrates

Expertise

I can answer any questions from the standard four semester Calulus sequence. Derivatives, partial derivatives, chain rule, single and multiple integrals, change of variable, sequences and series, vector integration (Green`s Theorem, Stokes, and Gauss) and applications. Pre-Calculus, Linear Algebra and Finite Math questions are also welcome.

Experience

Ph.D. in Mathematics and many years teaching undergraduate courses at three state universities.

Education/Credentials
B.S. , M.S. , Ph.D.

©2012 About.com, a part of The New York Times Company. All rights reserved.