Finding intervals of unit length on which f(x) has it's zeros

[The_Iceflash]

Homework Statement

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]

Homework Equations

N/A

The Attempt at a Solution

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.

 

[The_Iceflash]

Please? Anyone?