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Sagot :
Consider the next polynomial function,
[tex]\begin{gathered} f(x)=(x+1)(x^2+1) \\ \Rightarrow f(x)=(x+1)(x-i)(x+i) \end{gathered}[/tex]Notice that f(x) has one real zero and two complex zeros.
However, the expanded form of f(x) is
[tex]f(x)=x^3+x^2+x+1[/tex]Therefore, f(x) is a polynomial of degree 3 with real coefficients that has exactly 1 real zero and 2 complex zeros.
This is a counterexample of the statement. The answer is False.
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