CJG123 2 years ago how do i find the zeros of f(x)=x^3-3x^2-3?

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1. lordcyborg

find a zero by hit and trial method. Next u get a factor so divide by it and then find the rest of the zeroes

2. AKANicole

hum i now this!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

this can not be factored! http://www.wolframalpha.com/input/?i=x%5E3+-+3x%5E2+-+3+%3D+0

4. oldrin.bataku

@RadEn indeed this is not reducible over the reals... check the discriminant.

actually the discriminant used in quadratic equation, not for cubic eq

6. lordcyborg

7. oldrin.bataku

@RadEn the discriminant you are likely familiar with is $$\Delta=b^2-4ac$$, and it is (indeed) only for quadratic equations $$ax^2+bx+c=0$$. But the discriminant as a concept is extended to polynomials of other degree... http://en.wikipedia.org/wiki/Discriminant For example, a cubic equation $$ax^3+bx^2+cx+d=0$$ yields a discriminant $$b^2c^2-4ac^3-4b^3d-27a^2d^2+18abcd$$, a homogeneous polynomial of degree 4.

8. oldrin.bataku

http://en.wikipedia.org/wiki/Cubic_polynomial#The_nature_of_the_roots So let us check our discriminant now :-)$$\Delta=b^2c^2-4ac^3-4b^3d-27a^2d^2+18abcd$$Here, we have $$x^3-3x^2-3=0$$ so $$a=1, b=-3,c=0,d=-3$$. Plug them in:\begin{align*}\Delta&=27(1)^2(-3)^2-4(1)(0)-4(-3)^3(-3)-27(1)^2(-3)^2+18(1)(-3)(0)(-3)\\&=27\times9-0-4\times81-27\times9+0\\&=-4\times81\lt0\end{align*}Because $$\Delta\lt0$$, we have only one real root and two complex conjugate roots.

9. lordcyborg

No need of such big discriminants coz one can always use hit and trial method to find the zero of a simple equation like this..... and then use the discriminant for the quadratic equation after creating a factor with that zero.

10. oldrin.bataku

@lordcyborg the real root is not trivial here, so tell me more about how you plan on using a simple "hit and trial" method :-) In fact, this polynomial's only real root isn't rational.

11. lordcyborg

hmmmm @oldrin.bataku I did not take a good look at d equation. So I suggested to use just hit and trial method. Yup u r correct. Sorry for arguing!!!!!!

12. oldrin.bataku

@lordcyborg no argument here! Just discussing math :-p