Answer
$x=-4.04$
Work Step by Step
$f(x)=2x^{3}+6x^{2}-8x+2=0$
Work shown in image below.
Subdivide the interval $[-5,-4]$ into 10 subintervals and find f(each endpoint).
We find opposite signs on endpoints of $[-4.1,-4.0 ]$.
By the Intermediate Value Theorem, a real zero is inside that interval.
Subdivide the interval $[-4.1,-4.0 ]$ into 10 subintervals and find f(each endpoint).
We find opposite signs on endpoints of $[-4.05,-4.04]$.
So a real zero is $x=-4.04...$
Correct to 2 decimal places : $x=-4.04$
