- #1
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?
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.
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.
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.
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.
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.