Cubic and Quartics, solving methods?

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In summary, cubic and quartic equations are types of polynomials with three and four terms respectively, involving variable raised to the third and fourth power. The most common methods for solving these equations are factoring, quadratic formula, and Cardano's method. The choice of method depends on the form of the equation. Special cases for solving these equations include equations with complex or repeated roots, and depressed equations without a term with a power of x. These equations can also be solved using a graphing calculator, but it may not be as accurate as solving by hand.
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PrudensOptimus
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Instead of long ass "formulas" for Cubic and Quartics equations, can someone give some solving techniques? Perhaps in the end attach the formula just in case your hand gets itchy?
 
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if you don t want help, don t ask for it.

Edit: This post is a reply to an impolite comment by Prudens that has since been deleted.
 
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1. What are cubic and quartic equations?

Cubic and quartic equations are types of polynomials that involve a variable raised to the third and fourth power, respectively. They are called cubic and quartic because they have three and four terms, respectively.

2. What are some common methods for solving cubic and quartic equations?

The most common methods for solving cubic and quartic equations are the factoring method, the quadratic formula, and the Cardano's method. Other methods include the Rational Root Theorem, Descartes' Rule of Signs, and Newton's method.

3. How do you know which method to use for solving a cubic or quartic equation?

The method you choose will depend on the form of the equation. If the equation can be easily factored, then the factoring method may be the best option. If the equation is in the form of ax2 + bx + c = 0, then the quadratic formula should be used. If the equation is in the form of x3 + ax2 + bx + c = 0, then Cardano's method may be the most efficient.

4. Are there any special cases for solving cubic and quartic equations?

Yes, there are several special cases for solving cubic and quartic equations. These include equations with complex roots, equations with repeated roots, and equations with irrational roots. There are also specific methods for solving depressed cubic and quartic equations, which are equations that do not have a term with a power of x.

5. Can cubic and quartic equations be solved using a graphing calculator?

Yes, cubic and quartic equations can be solved using a graphing calculator. You can input the equation into the calculator and use the zero or root function to find the x-intercepts, which are the solutions to the equation. However, this method may not be as accurate as solving the equations by hand using the appropriate methods.

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