Use the boundedness theorem to determine whether the polynomial function satisfies the given condition.
-The polynomial $f ( x ) = x ^ { 5 } + 10 x ^ { 4 } - 25 x ^ { 3 } - 10 x ^ { 2 } + 24 x$ has no real zero less than $- 8$.
A) Yes, the boundedness theorem shows that the polynomial has no real zero less than $- 8$.
B) No, the boundedness theorem does not show that the polynomial has no real zero less than $- 8$

Question

Quizplus · Accepted Answer

The boundedness theorem can help determine the behavior of a polynomial at infinity but does not specifically provide information about the existence or non-existence of real zeros below a certain value, such as -8, without further analysis or application of other theorems.

Use the Boundedness Theorem to Determine Whether the Polynomial Function f(x)=x5+10x4−25x3−10x2+24xf ( x ) = x ^ { 5 } + 10 x ^ { 4 } - 25 x ^ { 3 } - 10 x ^ { 2 } + 24 xf(x)=x5+10x4−25x3−10x2+24x

Use the Boundedness Theorem to Determine Whether the Polynomial Function $f ( x ) = x ^ { 5 } + 10 x ^ { 4 } - 25 x ^ { 3 } - 10 x ^ { 2 } + 24 x$