use the intermediate value theorem to show that the polynomial ( f(x)=4x^{4}-10x^{2}+2 ) has a real zero between ( -1 ) and 0.
select the correct choice below and fill in the answer boxes to complete your choice.
a. because ( f(x) ) is a polynomial with ( f(-1)=square<0 ) and ( f(0)=square>0 ), the function has a real zero between ( -1 ) and 0.
b. because ( f(x) ) is a polynomial with ( f(-1)=square<0 ) and ( f(0)=square<0 ), the function has a real zero between ( -1 ) and 0.
c. because ( f(x) ) is a polynomial with ( f(-1)=square>0 ) and ( f(0)=square>0 ), the function has a real zero between ( -1 ) and 0.
d. because ( f(x) ) is a polynomial with ( f(-1)=square>0 ) and ( f(0)=square<0 ), the function has a real zero between ( -1 ) and 0.

Question

Accepted Answer

# Explanation:
## Step1: Calculate $f(-1)$
Substitute $x = - 1$ into $f(x)=4x^{4}-10x^{2}+2$.
$$
\begin{align*}
f(-1)&=4\times(-1)^{4}-10\times(-1)^{2}+2\
&=4\times1 - 10\times1+2\
&=4 - 10 + 2\
&=-4
\end{align*}
$$
## Step2: Calculate $f(0)$
Substitute $x = 0$ into $f(x)=4x^{4}-10x^{2}+2$.
$$
\begin{align*}
f(0)&=4\times0^{4}-10\times0^{2}+2\
&=0-0 + 2\
&=2
\end{align*}
$$

# Answer:
A. Because $f(x)$ is a polynomial with $f(-1)=-4<0$ and $f(0) = 2>0$, the function has a real zero between $-1$ and $0$.

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Question

Explanation:

Step1: Calculate \(f(-1)\)

Step2: Calculate \(f(0)\)

Answer: