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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

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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.

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