Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the
numbers given.
-$f ( x ) = 8 x ^ { 3 } + 9 x ^ { 2 } - 8 x - 5 ; - 2$ and $- 1$
A) $f ( - 2 ) = 17$ and $f ( - 1 ) = - 4$
B) $f ( - 2 ) = - 16$ and $f ( - 1 ) = 5$
C) $f ( - 2 ) = - 17$ and $f ( - 1 ) = 4$
D) $f ( - 2 ) = 17$ and $f ( - 1 ) = 4$

Question

Quizplus · Accepted Answer

The Intermediate Value Theorem states that if a continuous function changes sign over an interval, it must have a zero in that interval. Here, $f(-2) = -17$ and $f(-1) = 4$, indicating a sign change, so there is a real zero between -2 and -1.

Use the Intermediate Value Theorem for Polynomials to Show That f(x)=8x3+9x2−8x−5;−2f ( x ) = 8 x ^ { 3 } + 9 x ^ { 2 } - 8 x - 5 ; - 2f(x)=8x3+9x2−8x−5;−2

Use the Intermediate Value Theorem for Polynomials to Show That $f ( x ) = 8 x ^ { 3 } + 9 x ^ { 2 } - 8 x - 5 ; - 2$