How can the Intermediate Value Theorem be used to find a root of a polynomial?

[Dynex]

Hey i was jus wondering how to solve this equation i need to find a value of x when subsituted in the eqn is less than 0 so a negative value and a value of x when substituted into the eqn is greater than 0 so a positive value
this will prove that a root exists between those domains (ie. Intermediate value theorem)

p(x)=60x(1+x)^72-(1+x)^72+1

Thankz for the help

 

[rocomath]

if you're trying to test for a # greater/less than 0, just set your equation equal to 0 and solve for x. then choose values greater/less than the value you found.

 

[Dynex]

hey yea that's wa i was plannin on doing but since its like ^72 i can't figure that part out

 

[EnumaElish]

Just by staring at p(x) you can tell one root. Can you guess?

 

[Dynex]

is it 0 -1 or 1

 

[EnumaElish]

Whcih do you think?

 

[Dynex]

hmmm ill go with -1 ?

 

[EnumaElish]

Okay, plug in x = -1. What do you get?

 

[rocomath]

"middle-term"

 

[Dynex]

i got a value of 1

 

[Dynex]

which is greater than 0 so now i need to find a value where f(x)<0

 

[Dynex]

any ideas?

 

[EnumaElish]

I'd try the next integers to either side.

 

[Dynex]

when i tried 2 , 3 and four i got really large numbers

 

[EnumaElish]

You are not paying attention to the polynomial's terms.