blu3fan wrote:Find the roots of: z^3 + 6z^2 - 4z - 24 = 0
Consider the associated polynom:
It' s easy to see that f(2) = 2^3 + 6*2 ^2 - 4*2 - 24 = 8 + 36 - 8 - 24 = 0.
From Bezout theorem you have that if a is a root of a polynom anX^n + ... + a1x + a0, with a0, a1, ..., an real coefficients, then that polynom is divided by (X-a).
divisible with (z-2). Putting the fraction and making the division, you get:
We can find the other 2 solutions of your equation, by finding the roots of
, where we have
, where a,b, c in R, a not Null.
On our example, a = 1, b = 8, c = 12.=>