In order for this to be correct we would need \(\displaystyle \sqrt[3]{ 0.125 - 0.5 } = 0\), which clearly isn't true. Is there a typo?STS said:
First, identify the given cubic equation and make sure it is in the form of ax^3 + bx^2 + cx + d = 0. Then, use the rational root theorem to find possible rational roots. Next, use synthetic division to test each possible root until you find one that works. Once you have found one root, use the quadratic formula to solve for the remaining roots.
The rational root theorem states that any rational root of a polynomial equation will be a factor of the constant term divided by a factor of the leading coefficient. This helps by giving a list of possible rational roots to test in the equation, making it easier to find a root and solve the equation.
Yes, the quadratic formula can be used to solve a cubic root algebra problem, but only after one root has been found using the rational root theorem and synthetic division. The quadratic formula can then be used to solve for the remaining roots.
Synthetic division is a shortcut method for dividing polynomials by a linear factor. It helps with solving cubic root algebra by allowing you to quickly test possible rational roots and find one that works. This saves time and makes the process of solving a cubic root algebra problem more efficient.
Yes, there is a specific order in which you should solve a cubic root algebra problem. First, use the rational root theorem to find possible rational roots. Then, use synthetic division to test each possible root until you find one that works. Once you have found one root, use the quadratic formula to solve for the remaining roots. Finally, check your solutions by plugging them back into the original equation to ensure they are correct.
