Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the
numbers given.
-$f ( x ) = x ^ { 4 } - 9 x ^ { 2 } + 18 ; 1.7$ and $1.8$
A) $f ( 1.7 ) = 0.3421$ and $f ( 1.8 ) = - 0.6624$
B) $\mathrm { f } ( 1.7 ) = 0.3421$ and $\mathrm { f } ( 1.8 ) = 0.6624$
C) $f ( 1.7 ) = - 0.3421$ and $f ( 1.8 ) = - 0.6624$
D) $f ( 1.7 ) = 0.6579$ and $f ( 1.8 ) = - 0.6624$

Question

Quizplus · Accepted Answer

The Intermediate Value Theorem states that if a function $f$ is continuous on a closed interval $[a, b]$ and $N$ is any number between $f(a)$ and $f(b)$, then there is at least one number $c$ in the interval $[a, b]$ such that $f(c) = N$. For the polynomial $f(x) = x^4 - 9x^2 + 18$, we can see that $f(1.7) = 0.3421$ and $f(1.8) = -0.6624$, indicating a change in sign from positive to negative. This change in sign means there must be at least one real zero between $x = 1.7$ and $x = 1.8$, confirming the statement in choice A.

Use the Intermediate Value Theorem for Polynomials to Show That f(x)=x4−9x2+18;1.7f ( x ) = x ^ { 4 } - 9 x ^ { 2 } + 18 ; 1.7f(x)=x4−9x2+18;1.7

Use the Intermediate Value Theorem for Polynomials to Show That $f ( x ) = x ^ { 4 } - 9 x ^ { 2 } + 18 ; 1.7$