Solving Quadratic Equation Using Box Factoring

In summary, the conversation is about a question on finding the roots or zeroes of a quadratic function using the Box Method. The person asking the question tried to use the method shown on a website but encountered an error in the factored down version of the equation. They were wondering if the method works for this particular equation and asked for help in identifying their mistake. The solution is to take out the common factor first before factoring.
  • #1
nordqvist11
15
0

Homework Statement




f(x)=6x^2+9x-6

Where does this function intersect the x-axis (i.e. what are the roots or zeroes of f(x))?

Solve by factoring using the Box Method. When I use the method that is shown on this website http://www.purplemath.com/modules/factquad2.htm for this particular problem I end up with this as my factored down version of the equation.
(6x-3)(3x+6)
But that is wrong because I would end up with 18x^2 as my leading term instead of the 6x^2 (which is in the desired equation) when I FOIL them out.

My question is that does using the method on that website to factor down a quadratic work for this equation? If so, could someone tell me what I'm doing wrong.

Thanks :)

Homework Equations





The Attempt at a Solution


[PLAIN]http://5img.com/img836/4599/69quadproblem.jpg
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Welcome to PF, nordqvist11! :smile:

Your equation looks like the last example on the page you mentioned.
It says there that you should take out the common factor first...
 
  • #3
You're right it does :). Thanks a lot, I got a real headache because of that.
 

1. What is box factoring?

Box factoring is a method used to solve quadratic equations by creating a box or grid and filling in the coefficients of the equation. This allows for a visual representation of the equation, making it easier to factor and solve.

2. How do you use box factoring to solve a quadratic equation?

To use box factoring, you first write the equation in the form ax^2 + bx + c = 0. Then, create a box or grid with four sections. Fill in the first section with the coefficient of the x^2 term, the last section with the constant term, and the middle sections with the coefficients of the x term. From there, you can use a combination of factoring and algebraic manipulation to solve for the roots of the equation.

3. What are the advantages of using box factoring over other methods?

Box factoring can be helpful for visual learners as it provides a visual representation of the equation, making it easier to understand and solve. It also allows for a systematic approach to factoring, making it less prone to mistakes compared to other methods.

4. Can all quadratic equations be solved using box factoring?

No, not all quadratic equations can be solved using box factoring. This method is most effective for equations with integer coefficients and a leading coefficient of 1. For equations with non-integer coefficients or a leading coefficient other than 1, other methods such as quadratic formula or completing the square may be more useful.

5. Are there any tips for using box factoring effectively?

One tip for using box factoring effectively is to always make sure the equation is in standard form before beginning. This means that the terms should be arranged in descending order of degree, with the x^2 term first, followed by the x term, and then the constant term. It is also helpful to double check your work and make sure all sections of the box are correctly filled in before proceeding to solve the equation.

Similar threads

Maximizing Area: Solving Quadratic Applications with Triangles and Rectangles
    • Precalculus Mathematics Homework Help
Replies
23
Views
2K
Find the value of ##r## and ##s## in the given quadratic equation
    • Precalculus Mathematics Homework Help
Replies
1
Views
916
Solve the given equation that involves fractional indices
    • Precalculus Mathematics Homework Help
2
Replies
39
Views
2K
Quadratic function minimal value
    • Precalculus Mathematics Homework Help
Replies
11
Views
1K
Solve the quadratic equation that involves sum and product
    • Precalculus Mathematics Homework Help
Replies
1
Views
774
Formula for Xo and Yo for graph of quadratic function
    • Precalculus Mathematics Homework Help
Replies
2
Views
856
Both roots of a quadratic equation lying within limits
    • Precalculus Mathematics Homework Help
Replies
22
Views
2K
Quadratic equation and its roots
    • Precalculus Mathematics Homework Help
Replies
14
Views
1K
Solve the simultaneous equations
    • Precalculus Mathematics Homework Help
Replies
7
Views
1K
Expressing Quadratic Equations in Different Forms
    • Precalculus Mathematics Homework Help
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top