- #1
ollie456
- 9
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Can anyone help solve S3+101S2+(10K+100)S+100K to find the roots of S in terms of K
A cubic equation is a polynomial equation of the form ax^3 + bx^2 + cx + d = 0, where a, b, c, and d are constants and x is the variable. It is called a cubic equation because it involves a variable raised to the third power (cubed).
There are several methods for solving a cubic equation, including the rational root theorem, synthetic division, and the cubic formula. The most commonly used method is the cubic formula, which involves finding the roots (or solutions) of the equation by using a specific formula.
The cubic formula, also known as the Cardano formula, is a method for finding the roots of a cubic equation. It involves finding the roots of a depressed cubic equation (one in which the coefficient of the x^2 term is zero) and then using those roots to find the roots of the original equation. The formula is quite complex and involves the use of complex numbers.
Yes, there are two special cases when solving a cubic equation: when the equation has a double root (two of the three roots are equal) and when the equation has three real roots. In the case of a double root, the cubic formula can be simplified and in the case of three real roots, the roots can be found using the rational root theorem.
No, not all cubic equations can be solved using the cubic formula. Some cubic equations have irrational (non-repeating, non-terminating) solutions that cannot be expressed using radicals (square roots, cube roots, etc.). These equations are known as irreducible cubics and cannot be solved using traditional methods.