Provide an appropriate response.
-What is the minimum number of x intercepts that a polynomial of degree 11 can have? Explain.
A) 11 because this is the degree of the polynomial.
B) 1 because a polynomial of odd degree crosses the x axis at least once.
C) 0 because a polynomial of odd degree may not cross the x axis at all.
D) Not enough information is given.

Question

Quizplus · Accepted Answer

A polynomial of odd degree must cross the x-axis at least once due to the Intermediate Value Theorem, which states that if a polynomial function is continuous over a closed interval and changes sign over that interval, then there is at least one root (x-intercept) within that interval. Since an 11th degree polynomial will go from negative infinity to positive infinity (or vice versa), it must cross the x-axis at least once.

Provide an Appropriate Response