## Finding intervals of unit length/bisection method

1. The problem statement, all variables and given/known data
a) Find the intervals of unit length on which $f(x) = 2x^4-8x^3+24x-17$ has it's zeros.

b) For each of the following starting intervals, tell which of the zeros of f(x) will be found by the bisection method associated with the proof of Bolzano's Theorem. (Label the zeros x1 < x2 < x3 < x4 .)

(i) [-4,2]
(ii) [-2,4]
(iii) [0,4]

So here's what I did thus far:

x|y
-2|31
-1|-31

root somewhere in [-2,-1]

x|y
0|-17
1|1

root somewhere in [0,1]

x|y
1|1
2|-1

root somewhere in [1,2]

x|y
2|-1
3|1

root somewhere in [2,3]

[-2,-1] Midpoint = -3/2

2(-3/2)^4-8(-3/2)^3+24(-3/2)-17 = -15.875 [a1, b1] = [-3/2,1]

[0,1] Midpoint = 1/2

2(1/2)^4-8(1/2)^3+24(1/2)-17 = -5.875 [a1, b1] = [1/2,1]

[1,2] Midpoint = 3/2

2(3/2)^4-8(3/2)^3+24(3/2)-17 = 2.125 [a1, b1] = [1,3/2]

[2,3] Midpoint = 5/2

2(5/2)^4-8(5/2)^3+24(5/2)-17 = -3.875 [a1, b1] = [5/2,3]

I've gotten this far but I'm not sure where to go next. Thanks.