# Rational roots

#### Miracles

can a non-factorable function has rational real roots?

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#### Hootenanny

Staff Emeritus
Science Advisor
Gold Member
can a non-factorable function has rational real roots?
Yes, for example take $f(x):= x+a$ where $a \in \mathbb{Q}$.

#### StatusX

Homework Helper
Are you asking if a polynomial with rational coefficients which cannot be written as the product of polynomials with rational coefficients of smaller degree can have rational roots? Except for the trivial case of polynomials of degree one, the answer is no, because any rational root a of f(x) translates to a linear factor (x-a) of f(x), ie, there is a polynomial g(x) with rational coefficients such that f(x)=(x-a)g(x).

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