The discussion revolves around solving the inequality 12x^3 + 8x^2 ≤ 3x + 2 and justifying the solution. Participants explore methods for addressing third-degree polynomials, including the use of the Rational Root Theorem and the creation of sign charts.
Participants generally agree on the steps to approach the problem, including the use of the Rational Root Theorem and the importance of a sign chart. However, the discussion remains unresolved regarding the specific methods and justifications needed for the inequality.
The discussion does not resolve the specific mathematical steps required to solve the inequality, and there are varying interpretations of the justification process.
Raerin said:Solve the inequality 12x^3 + 8x^2 ≤ 3x + 2 and justify your answer.
To justify the answer do you need to make a sin chart and graph it?
Oops, I made a typo, so yes, I do mean sign chart.I like Serena said:Hi Raerin! :)
The usual approach is to first solve the equality.
Then take the derivative and find its roots.
Then you can make a sign chart to read off the solution (did you mean a sign chart instead of a sin chart?)
The first step is already not so easy for this particular problem.
As Petrus suggested, the easiest way to find the roots is by using the Rational root theorem.
Do you know of it?
Raerin said:Oops, I made a typo, so yes, I do mean sign chart.
You're supposed to bring everything to one side, right? Then you find the number that would make the polynomial = 0?