Set up a polynomial with integer coefficients that each of the following numbers is a root and then use the rational root theorem to show that each of these is irrational. (a) 13 (b) 5+ √2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
2 Set up a polynomial with integer coefficients that each of the following numbers is a root of,
and then use the rational root theorem to show that each of these is irrational.
(a) 13
(b) 5+ √2
Transcribed Image Text:2 Set up a polynomial with integer coefficients that each of the following numbers is a root of, and then use the rational root theorem to show that each of these is irrational. (a) 13 (b) 5+ √2
Expert Solution
Step 1

First we convert the given number into the polynomial with integer coefficient.

Then we find all possible  roots.

Then we find that the possible roots equate polynomial to zero or not.

If possible roots are not equate zero to polynomial then that polynomial does not have any rational root i.e. it has irrational root.

Hence, the polynomial we find has only root which is given number and it is irrational.

steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,