Finding intercepts of a cubic function

[Arya1127]

Hey guys, new member here. I've decided to join this forum since I am a current Calculus student, and will be taking Physics next semester. Anyways, I do have a question about one of my homework problems.

Homework Statement

Consider the function: f(x) = -2x^(3) + 6x^(2) - 3. Find its intercepts (there is more to this problem, but this is all I'm concerned about)

Homework Equations

I understand finding x intercepts requires setting the equation equal to 0, but that doesn't help me in this case.

The Attempt at a Solution

I've tried different things, from factoring to polynomial division, but I can't find the answer. Anyways, the answers are (-0.64, 0), (0.83, 0), and (2.81, 0). I just need help on how to find these intercepts.

 

[symbolipoint]

Did you try Rational Roots Theorem? Your first listed expected answer at least appears that it would be found that way. You would then try to perform division of the function by the binomial obtained from use of Rational Roots Theorem, and you should have hopefully an easier quotient function to handle. You can always cheat and use a graphing calculator.

 

[HallsofIvy]

No, that has three real roots but none of them are rational. You will have to either use the Cardano's cubic formula, http://www.math.vanderbilt.edu/~schectex/courses/cubic/, or do a numerical calculation such as Newton's methods, http://en.wikipedia.org/wiki/Newton's_method