Using Bisection Method to Find Points of Intersection for y=x^3-2x+1 and y=x^2

In summary, the conversation is about using the bisection method to find the points of intersection of two curves. The question asks about how to apply the bisection method in this scenario, and the response suggests using an equation derived from the curves to find either the x or y value of the point of intersection. The conversation ends with the questioner stating that they have solved the problem.
  • #1
gomes.
58
0
[itex]y=x^3-2x+1[/itex]

[itex]y=x^2[/itex]


The question says to use the bisection method to find the points of intersection of the 2 curves. I know how to use the bisection method to find the root of an equation (like on this page http://kr.cs.ait.ac.th/~radok/math/mat7/step7.htm ), but how would I use it to find the point of intersection? Thanks.
 
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  • #2
Well let [tex](x_i,y_i)[/tex] be a point of intersection. Can you use those curves to derive an equation for which either [tex]x_i[/tex] or [tex]y_i[/tex] is a root?
 
  • #3
gomes. said:
question says to use the bisection method to find the points of intersection of the 2 curves. I know how to use the bisection method to find the root of an equation (like on this page http://kr.cs.ait.ac.th/~radok/math/mat7/step7.htm ), but how would I use it to find the point of intersection? Thanks.

What do you get if you subtract one equation from the other?
 
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  • #4
thanks, I've solved it now :)
 

1. What are points of intersection?

Points of intersection are points where two or more lines, curves, or surfaces meet or cross each other.

2. How do you calculate the coordinates of points of intersection?

The coordinates of points of intersection can be calculated by solving the equations of the lines, curves, or surfaces that are intersecting. This can be done by setting the equations equal to each other and solving for the variables.

3. What do points of intersection represent in real-world situations?

In real-world situations, points of intersection can represent the location where two roads cross, the point where two pipes intersect, or the point where two graphs on a coordinate plane meet.

4. Can points of intersection have multiple solutions?

Yes, points of intersection can have multiple solutions if there are multiple sets of coordinates that satisfy the equations of the intersecting lines, curves, or surfaces.

5. How do points of intersection relate to systems of equations?

Points of intersection are closely related to systems of equations, as solving for the points of intersection involves solving a system of equations. In a system of linear equations, the points of intersection represent the solution to the system, as they are the coordinates that satisfy all of the equations in the system.

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