Use the Intermediate Value Theorem for Polynomials to Show That $f ( x ) = 7 x ^ { 3 } + 9 x ^ { 2 } - 7 x + 4 ; - 2$

question 58

Multiple Choice

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

• A) \(f ( - 2 ) = - 2\) and \(f ( - 1 ) = 13\)
• B) \(f ( - 2 ) = 2\) and \(f ( - 1 ) = - 13\)
• C) \(f ( - 2 ) = - 1\) and \(f ( - 1 ) = 14\)
• D) \(f ( - 2 ) = 2\) and \(f ( - 1 ) = 13\)

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Definitions:

Pond

A small body of still water, typically smaller than a lake, formed naturally or by artificial means.

Shallow-Water

Areas of water that are not deep, often found near the shores of bodies of water, where sunlight can penetrate to the bottom, supporting various aquatic life.

Emergent Vegetation

Plants that grow in water but emerge above its surface, typically found in wetlands or shallow waters.

Stratification

The layering of sedimentary rock or soil with differing characteristics, or the arrangement of society into different social classes or castes.