I have known some Sufficient Condition for All the Roots of a Polynomial To Be Real. Is there any sufficient condition that a polynomial of degree $n$ has $n$ distinct roots? For $n=2$, it is trivial.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
Here's how it works:
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
The condition, over a field of characteristic 0 (or characteristic greater than the degree), is that the gcd of the polynomial and its derivative is 1.