How can I find the roots of a cubic equation?

[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

 

[symbolipoint]

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.

 

[symbolipoint]

(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.

 

[symbolipoint]

(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?

 

[James...]

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 definite! 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