Answer
$x=0.21.$
Work Step by Step
$f(x)=8x^{4}-2x^{2}+5x-1$
Work shown in image below.
Subdivide the interval $[0,1]$ into 10 subintervals and find
f(each endpoint).
We find opposite signs on endpoints of $[0.2,0.3]$.
By the Intermediate Value Theorem, a real zero is inside that interval.
Subdivide the interval $[0.2,0.3]$ into 10 subintervals and find f(each endpoint).
We find opposite signs on endpoints of $[0.21,0.22]$.
So a real zero is $x=0.21...$
Correct to 2 decimal places : $x=0.21.$