Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the
numbers given.
-$f ( x ) = - 7 x ^ { 4 } - 9 x ^ { 3 } - 4 x - 5 ; - 1$ and 0
A) $f ( - 1 ) = - 1$ and $f ( 0 ) = 5$
B) $f ( - 1 ) = 1$ and $f ( 0 ) = - 5$
C) $f ( - 1 ) = - 1$ and $f ( 0 ) = - 5$
D) $f ( - 1 ) = 2$ and $f ( 0 ) = - 4$

Question

Quizplus · Accepted Answer

The intermediate value theorem states that if a continuous function changes sign over an interval, there is at least one real zero in that interval. Here, $f(-1) = 1$ and $f(0) = -5$, indicating a sign change, so there is a real zero between -1 and 0.

Use the Intermediate Value Theorem for Polynomials to Show That f(x)=−7x4−9x3−4x−5;−1f ( x ) = - 7 x ^ { 4 } - 9 x ^ { 3 } - 4 x - 5 ; - 1f(x)=−7x4−9x3−4x−5;−1

Use the Intermediate Value Theorem for Polynomials to Show That $f ( x ) = - 7 x ^ { 4 } - 9 x ^ { 3 } - 4 x - 5 ; - 1$