The discussion revolves around the solvability of two specific cubic polynomial equations: x^3 - x - 2 = 0 and x^3 + 9x - 1 = 0. Participants explore methods for determining their solvability, including algebraic and graphical approaches.
Participants express differing views on the methods for solving the cubic equations, with some advocating for synthetic division while others suggest evaluating the polynomials directly. There is no consensus on the best approach or on the specific solutions to the equations.
Some participants reference techniques like synthetic division and Cardano's method without fully resolving the implications of these methods for the specific polynomials discussed. The discussion includes assumptions about the solvability of cubic equations but does not clarify the conditions under which these methods apply.
davedave said:Here is a very difficult cubic polynomial.
x^3 - x - 2 = 0
I am wondering whether it is solvable or not. Please think about it.
aew782 said:I need help with this too I posted a similar one and haven't got a response... mine was x^3 + 9x -1=0...They are solvable, but I don't know how to get an answer algebraically or graphically.
symbolipoint said:Are they solvable? Let's have a guess: The first one can be tested for divisibility by x+1, x-1, x+2, and x-2. The second one can be tested for divisibility by x+1 and x-1. The results may be faster if you know synthetic division.