Answer
$x=-0.60.$
Work Step by Step
$f(x)=x^{4}+8x^{3}-x^{2}+2$
Work shown in image below.
Subdivide the interval $[-1,0]$ into 10 subintervals and find f(each endpoint).
We find opposite signs on endpoints of $[-0.7,-0.6 ]$.
By the Intermediate Value Theorem, a real zero is inside that interval.
Subdivide the interval $[-0.7,-0.6 ]$ into 10 subintervals and find f(each endpoint).
We find opposite signs on endpoints of $[-0.61,-0.60]$.
So a real zero is $x=-0.60...$
Correct to 2 decimal places : $x=-0.60.$
