Help please. Find all roots to the nearest 0.001 both graphically and algebraically
f(x)=x^4-3x^2+2x^2-7x-11

Question

Help please.  Find all roots to the nearest 0.001 both graphically and algebraically 
f(x)=x^4-3x^2+2x^2-7x-11

tkhunny · Answer

What's your plan?  I'm guessing that neither x = 11 nor x = 1 is a root, so the hunt for irrational roots commences.

abb0t · Answer

start by adding the 3x$^2$ and 2x$^2$..

anonymous · Answer

no my bad its 3x^3+2x^2

abb0t · Answer

if you fsctor out an x, you get: x[(x-2)(x-1)x-7]-11

mathstudent55 · Answer

I wonder what scale graph you need to use to be able to read a point to the nearest 0.001.

abb0t · Answer

lol. right?

tkhunny · Answer

It quartic, with positive 1st coefficient.  Thus, it wanders off without bound in a positive direction as x increases in either direction.  Thus, anything found to be negative wouls be interesting.  Clearly f(0) = -11

A quick catalogue:

f(0) = -11
f(1) = -18 -- Well, that was the wrong way.
f(2) = -25
f(3) = -14 -- It's turning around.
f(4) = 57 - and x = 4 is also an upper bound, so we can quit looking.

There's one between x = 3 and x = 4

f(-1) = 2 and x = -1 is a lower bound, so we can quit looking.

There's one between x = 0 and x = -1

How do you propose we find these guys?