Definition -1: Any polynomial $f(x)\in F[x]$ is called separable if all the irreducible factors of $f(x)$ are separable. Definition -1 is from 'Pearson' publication Modern Algebra and Definition-2 is from 'Dummit and Foote'.
Definition -2: A polynomial is said to be separable over $F$ if it has no multiple roots( i.e., all its roots are distinct).
According to Definition -1 $f(x)=(x-2)^3(x^2-2)$ over $\Bbb{Q}$ is separable. But this example contradicts the Definition -2.
Am I wrong some where? Or the definition of book is wrong.
Any help will be appreciated. Thanks!