Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the
numbers given.
-$f ( x ) = 8 x ^ { 5 } - 9 x ^ { 3 } + 6 x ^ { 2 } - 8 ; 1$ and 2
A) $f ( 1 ) = 3$ and $f ( 2 ) = 200$
B) $f ( 1 ) = - 2$ and $f ( 2 ) = 201$
C) $f ( 1 ) = - 3$ and $f ( 2 ) = 200$
D) $f ( 1 ) = 3$ and $f ( 2 ) = - 200$

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, $f(1) = -3$ and $f(2) = 200$, indicating a sign change, so there is a real zero between 1 and 2.

Use the Intermediate Value Theorem for Polynomials to Show That f(x)=8x5−9x3+6x2−8;1f ( x ) = 8 x ^ { 5 } - 9 x ^ { 3 } + 6 x ^ { 2 } - 8 ; 1f(x)=8x5−9x3+6x2−8;1

Use the Intermediate Value Theorem for Polynomials to Show That $f ( x ) = 8 x ^ { 5 } - 9 x ^ { 3 } + 6 x ^ { 2 } - 8 ; 1$