Is it possible for a degree #4# polynomial function to have one zero and its corresponding equation to have #4# roots? Explain.
Yes and no...
When we are counting roots or zeros, we may or may not include multiplicity in our count.
Consider for example, the quartic function:
#f(x) = x^4#
This function is zero for only one value of
The corresponding equation is:
#x^4 = 0#
By the Fundamental Theorem of Algebra, any quartic equation in one variable has exactly
There are reasons to count roots or zeros according to their multiplicity or not. It really depends on the context.
So we could say that
Zeros always correspond to roots and vice versa, but the convention for each concerning multiplicity may vary.