Mathematics via Problems - Algebra

by Skopenkov

Solving Polynomial Equations of Degree 3 and 4

3.2.5. Vieta’s method.

(a) Solve $4x^3-3x=\frac{1}{2}$. (b) Solve $x^3-3x-1=0$. (c) Use the cosine and inverse cosine functions to devise a general formula for the solution of $x^3+px+q=0$ by the method outlined in these problems. Under what conditions can $x^3+px+q=0$ be solved by this method?