Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
-$$f ( x ) = - 6 x ^ { 4 } - 3 x ^ { 2 } + 6 ; [ - 1,0 ]$$
A) $f ( - 1 ) = 3$ and $f ( 0 ) = 7$; no
B) $f ( - 1 ) = - 3$ and $f ( 0 ) = - 6$; no
C) $f ( - 1 ) = 3$ and $f ( 0 ) = - 6$; yes
D) $f ( - 1 ) = - 3$ and $f ( 0 ) = 6$; yes

Question

Quizplus · Accepted Answer

Calculating $f(-1)$ and $f(0)$ gives $f(-1) = -3$ and $f(0) = 6$. Since the function changes sign from negative to positive in the interval $[-1,0]$, by the Intermediate Value Theorem, there must be at least one zero in this interval.

Use the Intermediate Value Theorem to Determine Whether the Polynomial f(x)=−6x4−3x2+6;[−1,0]f ( x ) = - 6 x ^ { 4 } - 3 x ^ { 2 } + 6 ; [ - 1,0 ]f(x)=−6x4−3x2+6;[−1,0]

Use the Intermediate Value Theorem to Determine Whether the Polynomial $f ( x ) = - 6 x ^ { 4 } - 3 x ^ { 2 } + 6 ; [ - 1,0 ]$