Question

A polynomial of degree three has:

• A. Only one zero
• B. Exactly three zeroes
• C. Almost three zeroes
• D. More than three zeroes

Hint:

A cubic polynomial (degree 3) always has exactly three zeroes, but they may not be distinct and could be real or complex.

Answer 1

The Correct Option is B

A polynomial of degree three, which is a cubic polynomial, can have exactly three zeroes. These zeroes could be real or complex, and they may or may not be distinct.
Step 2: Analyzing the options.
\begin{itemize} \item (A) Only one zero: Incorrect. A cubic polynomial cannot have just one zero. It has exactly three, though some of them might be repeated. \item (B) Exactly three zeroes: Correct. A cubic polynomial always has exactly three zeroes. \item (C) Almost three zeroes: Incorrect. A cubic polynomial has exactly three zeroes, not "almost" three. \item (D) More than three zeroes: Incorrect. A cubic polynomial can have at most three zeroes. \end{itemize}
Step 3: Conclusion.
Therefore, the correct answer is (B) Exactly three zeroes. Final Answer:} Exactly three zeroes.