Answer
$f(-1)$ and $f(0)$ have opposite signs,
so f(x) has a real zero between $-1$ and $0$.
Work Step by Step
The Intermediate Value Theorem for Polynomial Functions$:$
Let $f$ be a polynomial function with real coefficients.
If $f(a)$ and $f(b)$ have opposite signs,
then there is at least one value of $c$ between $a$ and $b$ for which $f(c)=0$.
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$ a=-1,\quad f(a)=(-1)^{4}-4(-1)^{2}+1=-2\quad$(negative)
$ b=0,\quad f(b)=(0)^{4}-4(0)^{2}+1=1\quad$(positive)
$f(-1)$ and $f(0)$ have opposite signs,
so f(x) has a real zero between $-1$ and $0$.
