# Thread: bisection method .. solving equation ?

1. ## bisection method .. solving equation ?

Bisection method .. solving equation:

$\displaystyle x^3-9x+1$

2. First of all, what you have is not an equation, but an expression.

Are you trying to solve for $\displaystyle \displaystyle x$ in the equation $\displaystyle \displaystyle x^3 - 9x + 1 = 0$? Or is it equal to some other number?

3. What you wrote is not an equation, it's an expression.

"bijection method" - well, you have to transform *stuff*=*stuff, stuff* in something like f(x)=f(y) and then prove that f is bijective (evidently, you chose a convenient function), so x=y. Then solve the new equation

Edit: o.o I was absolutly sure there is write "bijection". Sorry.

4. Originally Posted by veileen
What you wrote is not an equation, it's an expression.

"bijection method" - well, you have to transform *stuff*=*stuff, stuff* in something like f(x)=f(y) and then prove that f is bijective (evidently, you chose a convenient function), so x=y. Then solve the new equation
The OP is asking for help with the BiSection method... In other words, continually cutting the region that the root falls in in half so that you close in on the root.

5. does it belong to integration or differentiation ?

and what is a differential equation ... this is tough

6. Originally Posted by thomaztriz
does it belong to integration or differentiation ?

and what is a differential equation ... yehova my lord .. this is tough
It belongs to neither. And a differential equation is an equation that involves derivatives. Your equation does not have any.

7. The first thing you need to do is find an interval in which you know there is a solution.

If we let $\displaystyle f(x)= x^3- 9x+ 1$, it's easy to see that f(0)= 0- 9(0)+ 1= 1> 0 and that f(1)= 1- 9+ 1= -7< 1. Since the value of this continous equation is postive at 0 and negative at 1, there must be a solution between them.

Now "bisection" means "cutting in half. Half way between 0 and 1 is, of course, 1/2. What is f(1/2)?

(Actually this is a surprisingly simple problem!)

8. thanks a lot .. nice

for a moment i was thinking about that equation ..

and the derivatives ... and the integrals .. and the fundamental theorem of calculus .. ( do i make any sense?)

then the differential equations ?

and after that the numerical methods ..

i wish all this stuff was much clearer ..