Prove that for all real numbers c, if c is a root of a

Chapter 4, Problem 32E

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QUESTION:

Problem 32E

Prove that for all real numbers c, if c is a root of a polynomial with rational coefficients, then c is a root of a polynomial with integer coefficients.

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QUESTION:

Problem 32E

Prove that for all real numbers c, if c is a root of a polynomial with rational coefficients, then c is a root of a polynomial with integer coefficients.

ANSWER:

Solution

Step 1

In this problem, we have to prove that for all real numbers c, if c is a root of a polynomial with rational coefficients, then c is a root of a polynomial with integer coefficients.

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