# Roots of a cubic equation

• James...

#### James...

I've been looking at some practise exams for the University I would like to apply to, I have to sit the exam on 4th November.

We have never done finding the roots of a cubic equation before and I cannot figure it out from looking on the internet, the formulas are all horrible to understand.

Any help would be appreciated.

James

Knowing many formulas does not help. What helps is finding the linear binomial factors and any nonfactorable quadratic factors; and equate the whole expression to zero. You are interested in where the function equals zero, or where the function shares a point with the x-axis.

Your wish for knowing "formulas which are horrible to understand" reflects ones first-through study of College Algebra, in which you learn to deal with Descartes Law of Signs, Rational Roots Theorem, the Factor and Remainder Theorems. You could spend a good 2 months studying this stuff from a College Algebra textbook and become very well knowledgeable about these things. You really want to KNOW this stuff and you are not really concerned with a course grade for credit. Those laws and theorems really CAN be well learned if you spend the time seriously studying them; keeping the knowledge several weeks later is another thing entirely.

(CONTINUED)...
Actually for just a cubic equation, you don't need those fancy formulas. Usually, you would be expected to factor into linear and possibly a quadratic factor and determine what values of the variable make the product equal to zero.

(one more thought)
You could resort to Rational Roots Theorem and polynomial division, but not much else would be needed. Do you need an example?

Many many thanks for your replies, I think I will try and have a go at studying the things you mentioned in your first post for definate! Anything that will expand my knowledge and help me at University can only be a good thing!

I managed to get the answer by creating a linear and quadratic factor of the cubic equation. We have done this before many times, but never as part of a polynomial, I should have realized I could have done it as it equals zero and therefore I can split it into factors.

I will have a play about with the Rational Roots theorum and polynomial division tomorrow but I may need an example depending on how i find it.

Thanks again
James