On a relation between boundedness and degree boundedness of a sequence of polynomials

Our aim in this article is to show that under some conditions, a sequence {fn} of polynomials in R[x] is bounded on [a,b] only if the sequence {deg(fn)} of their degrees is unbounded. As an application of this we will then prove that for some families of polynomial functions y=f(x) there exists a vertical strip containing no maxima points of the y=|f(x)| functions.