- #1
- 679
- 30
Given a polynomial ##f(x)##. Suppose there exists a value ##c## such that ##f(c)=f'(c)=0##, where ##f'## denotes the derivative of ##f##. Then ##f(x)=(x-c)^mh(x)##, where ##m## is an integer greater than 1 and ##h(x)## is a polynomial.
Is it true? Could you prove it?
Note: The converse is true and can be proved easily.
Is it true? Could you prove it?
Note: The converse is true and can be proved easily.