## College Algebra (10th Edition)

$x=-4.04$
$f(x)=2x^{3}+6x^{2}-8x+2=0$ 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 : $x=-4.04$