# Finding roots of cubing equation

Find all roots of the following polynomial:

$$x^3 + x^2 + 1$$

-
What level of math are you studying? – ajotatxe Apr 21 '14 at 17:18
You can use cardon's method to find roots. – Satvik Mashkaria Apr 21 '14 at 17:18
@ Satvik Mashkaria. How? – voca Apr 21 '14 at 17:22
See cubic formula. – Lucian Apr 21 '14 at 19:42

Hint:

Use Cardano's Method. It's easy, trust me! (>‿◠)✌

-
ooh Full answer thanks ! – voca Apr 21 '14 at 17:24
Don't forget accept my answer @mol. (ô‿ô) – Anastasiya-Romanova 秀 Apr 21 '14 at 17:25

You can use the formulas of Cardano equation but not for sheep, because the form of the equation which is elected by the Cardano formulas is: $$x^3+px+q=0$$

If the equation is of the form: $$x^3+ax^2+bx+c=0$$ Your equation is the form of the above, therefore, by means of substitution $$x+\frac{a}{3}=y$$ acquired forms: $$y^3+\alpha y +\delta=0$$ where $$\alpha=-3\left(\frac{a}{3}\right)^2+b; \beta=-\left(\frac{a}{3}\right)^3+c; \delta=-\alpha\frac{a}{3}+\beta$$ i.e You should be solving the equation: $$27y^3-9y+2=0$$ using formulas of Cardano

-
Thanks...................... – voca Apr 21 '14 at 17:41