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Our teacher provided us a review packet for a test tomorrow. There is one equation/question that has me stumped.

I am given the equation f(x)= x^3-x^2-12, and asked to find the zeros for this. Now, I first looked at substituting a variable (say t) for x^2, but that won't work because it is of degree 3.

Next, I tried adding variables then regrouping, to see if I could factor out a root, but that does not work either. It would work if the equation was x^3+x^2-12, but alas it is not.

I even tried using my calculator once I found the factors of p and q (rational root theorem), but that got me nowhere.

I believe the answer is that you cannot find the roots using simple methods, but my teacher seems to feel you can.

Can you provide any help?

For the equation provided, it has one real root with value 2.676 (correct to 3 dp) and two complex conjugate roots.

In such an instance, your methods suggested will not be feasible. Even the rather light-touch approach of the factor theorem will not work.

One plausible way to solve this would be via the Newton-Raphson method, though I am unsure if you have been taught such a technique. It involves a preliminary educated guess for the value of one of the roots, and it definitely isn't a "simple" method.

My advice? Don't worry too much about this question.

Peace.

Algebra

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