How would you find the real and complex roots of x^3+x^2+x+2?

Question

I need to know the method, not just the answer.

Answer 1

You just need to know the method? And you want to know it in an hurry? May I laugh? Why don't you read this wiki article about cubic equations, and how to find the algebraic roots of them.

Here's the one real root to this equation:

-1/3 -2/3 (2/(-47+3Sqrt(249)))^1/3 + 1/3(1/2(-47+3Sqrt(249))^1/3

Of course, you can try to solve it through methods of approximations.

If the equation had read: x^3 + x^2 - x + 2, then immediately upon inspection, it can be seen that -2 is one of the roots, and so you divide this equation by x+2 to get x^2 - x + 1, a quadractic and easily solvable equation for the 2 remaining roots. But no, you want the other one, so life is rough.