Solving polynomials for variable (x)

In summary, the conversation is about finding centroids of 2d graphs using double integrals. The person is having trouble converting line equations and asks for useful methods to solve them. The other person suggests using geometry instead and the first person thanks them for the help.
  • #1
pearss
8
0

Homework Statement



I'm doing work finding the centroids of 2d graphs. I'm working these problems using double integrals of regions that are horizontally or vertically simple. To do this I have to be able to convert line equations from one variable to the other. Some are simple but others I'm having trouble with such as:

y = x + x^3

Are there any useful methods for solving for x in these difficult polynomials?

Thanks much
 
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  • #2
No. There's no simple way to solve a cubic. Why don't you give an example of the sort of problem you are trying to deal with? There may be a simpler way.
 
  • #3
oh i see. There is in fact another way (using geometry) but i was being stubborn and trying to force the double integrals. Thank you for the help sir :D
 

FAQ: Solving polynomials for variable (x)

What is a polynomial?

A polynomial is a mathematical expression that is made up of variables, coefficients, and exponents. It can have one or more terms, and the terms can be added, subtracted, or multiplied together.

How do you solve a polynomial for a variable (x)?

To solve a polynomial for a variable (x), you need to use algebraic techniques such as combining like terms, factoring, or using the quadratic formula. You will also need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

What are the steps to solve a polynomial for a variable (x)?

The steps to solve a polynomial for a variable (x) are:1. Simplify the polynomial by combining like terms.2. If there are parentheses, use the distributive property to remove them.3. If there are exponents, use the appropriate exponent rule to simplify them.4. If there are multiple variables, combine them using the distributive property.5. Set the polynomial equal to 0 and factor it.6. Use the Zero Product Property to find the solutions.7. Check your solutions by plugging them back into the original polynomial.

What are the different methods for solving a polynomial for a variable (x)?

There are several methods for solving a polynomial for a variable (x), such as:1. Combining like terms and simplifying.2. Using the distributive property.3. Factoring.4. Using the quadratic formula.5. Completing the square.6. Graphing.7. Using the rational roots theorem.

What are some common mistakes when solving polynomials for a variable (x)?

Some common mistakes when solving polynomials for a variable (x) include:1. Forgetting to follow the order of operations.2. Not distributing correctly.3. Making a mistake in factoring.4. Forgetting about negative solutions.5. Missing a step in the process.6. Not checking solutions.7. Making a calculation error.

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