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#### Raerin

##### Member
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?

#### Petrus

##### Well-known member
How do you solve third degree polynom? Do you know what rational root Theorem is?

#### Klaas van Aarsen

##### MHB Seeker
Staff member
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?

#### Raerin

##### Member
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?

#### Klaas van Aarsen

##### MHB Seeker
Staff member
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!