MHB Solve the inequality....and justify your answer

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To solve the inequality 12x^3 + 8x^2 ≤ 3x + 2, the first step is to rearrange the equation to set it to zero. The Rational Root Theorem can be used to find the roots of the polynomial, which is crucial for determining where the function changes sign. After finding the roots, taking the derivative helps identify critical points. A sign chart can then be created to analyze the intervals and justify the solution. This systematic approach ensures a comprehensive understanding of the inequality's behavior.
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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?
 
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How do you solve third degree polynom? Do you know what rational root Theorem is?
 
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?

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?
 
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?
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?
 
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?

Yep!
 
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