Answer
There exists a function that is a polynomial and does not have a real root.
Work Step by Step
Recall the definition of sufficient:
"$\forall x$, r(x) is a sufficient condition for s(x)" means "$\forall x$, if r(x) then s(x)."
In this case, r(x) is: function is a polynomial.
s(x) is: function has a real root.
Recall the form of the negation of a universal conditional statement:
$~(\forall x, P(x) \rightarrow Q(x)) \equiv \exists x$ such that $(P(x) \land $ ~$Q(x))$
In this case the negation is: "$\exists$ x such that r(x) and ~s(x)" which is, "there exists a function that is a polynomial and does not have a real root."
