Answer:
root estimate = 1.75
error bound = 0.25
Step-by-step explanation:
f is a polynomial, so it is continuous in R (real numbers). Then you can use Bolzano's theorem.
f(0) = -3.1 < 0
f(2) = 4 - 3.1 = 0.9 > 0
Then there exists c in [0, 2], for which f(c) = 0
In the bisection method you generate a sequence of approximations of a root. If you have a bracketing interval [a, b], such that
f(a) and f(b) have opposite signs, then you use approximate the root as
In this case:
Then:
The error bound is half the width of the interval [1.5, 2]