Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given.
-$f ( x ) = 2 x ^ { 3 } - 7 x ^ { 2 } + 4 x + 8 ; - 1$ and 0
A) $f ( - 1 ) = 5$ and $f ( 0 ) = - 8$
B) $f ( - 1 ) = - 4$ and $f ( 0 ) = 9$
C) $f ( - 1 ) = - 5$ and $f ( 0 ) = 8$
D) $f ( - 1 ) = 5$ and $f ( 0 ) = 8$

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. For choice C, $f(-1) = -5$ and $f(0) = 8$, indicating a sign change, thus there is a real zero between -1 and 0.

Use the Intermediate Value Theorem for Polynomials to Show That f(x)=2x3−7x2+4x+8;−1f ( x ) = 2 x ^ { 3 } - 7 x ^ { 2 } + 4 x + 8 ; - 1f(x)=2x3−7x2+4x+8;−1

Use the Intermediate Value Theorem for Polynomials to Show That $f ( x ) = 2 x ^ { 3 } - 7 x ^ { 2 } + 4 x + 8 ; - 1$