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) $f ( 1.7 ) = 0.6579$ and $f ( 1.8 ) = - 0.6624$
B) $f ( 1.7 ) = 0.3421$ and $f ( 1.8 ) = 0.6624$
C) $f ( 1.7 ) = - 0.3421$ and $f ( 1.8 ) = - 0.6624$
D) $f ( 1.7 ) = 0.3421$ and $f ( 1.8 ) = - 0.6624$

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. Here, $f(1.7) = 0.3421$ and $f(1.8) = -0.6624$, indicating a sign change, thus a real zero exists between 1.7 and 1.8.

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 $f ( x ) = x ^ { 4 } - 9 x ^ { 2 } + 18 ; 1.7$