I'm trying to find the root of $x^4-2x^3+5x^2-6=0$ in the interval $[1,2]$.
For $x_1$, can I use $1$ or $2$ since they're in the interval, or do I have to choose a number between $1$ and $2$?
I'm trying to find the root of $x^4-2x^3+5x^2-6=0$ in the interval $[1,2]$.
For $x_1$, can I use $1$ or $2$ since they're in the interval, or do I have to choose a number between $1$ and $2$?
To summarize what's been said in the comments, any value in the interval $[1,2]$ will give you the right root in this example. In general, though, you have to be a little more careful. See this question and its answers for more detail on what can go wrong if you make a bad guess.