# Thread: show solution exists in the interval

1. ## show solution exists in the interval

2x^(7)=1-x (0,1)????

2. ## Re: show solution exists in the interval

Originally Posted by sluggerbroth
2x^(7)=1-x (0,1)????
Are you familiar with the Intermediate Value Theorem?

We have $2x^7+x-1=0$. Consider the function $f(x)=2x^7+x-1$. We know that $f(0) = -1$ and $f(1) = 2$. Since $f$ is continuous, what does this tell us?

3. ## Re: show solution exists in the interval

i'm just learning IVT. not sure what ypu are saying about interval (0,1)

4. ## Re: show solution exists in the interval

Originally Posted by sluggerbroth
i'm just learning IVT. not sure what ypu are saying about interval (0,1)
What Reckoner pointed is that there is some "c" where 0 < c < 1 for which f(c) must be 0. In other words there exists atleast one root in (0,1).