trix1010 trix1010

26-04-2020
Mathematics

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Is a^2 - 39 prime...
a. Over the set of polynomials with rational coefficients?
b. over the set of polynomials with real coefficients?
c. Explain your answers to Parts a and b

Respuesta :

amna04352 amna04352

26-04-2020

Answer:

1) a) yes

b) no

c) a² - 39

(a)² - (sqrt(39))²

(a - sqrt(39))(a + sqrt(39))

This quadratic can be split into real factors, but not rational

sqrt(39) is a real number, but not rational since 39 is not a perfect square

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