Show a polynomial of degree n has at most n distint roots

[math8]

If F is a field, how do we prove that a non-zero polynomial with coefficients in F and of degree n has at most n distinct roots in F?

 

[WlfordBrimley]

have you tried induction on the degree of the polynomial?

 

[mathwonk]

e.g. can you do it for degree one polynomials?