Solve each polynomial inequality and express the solution set in interval notation. 2 s^2-5 s ≥3

Name: Problem 41, Chapter 0: Precalculus
Uploaded: 2020-06-30T20:33:26-08:00
Duration: 1 min 39 s
Channel: Linh Vu
Description: Solve each polynomial inequality and express the solution set in interval notation. 2 s^2-5 s ≥3

step 1 In this question, we're given the 2S square minus 5 S greater equal to the 3. The first time we

Solve each polynomial inequality and express the solution...

Key Concepts

Interval Testing

Once the zeros are identified, the next step is to test the sign of the polynomial in the intervals between these critical points. By choosing test points in each interval, one can determine whether the polynomial is positive or negative, thus identifying the solution set for the inequality.

Polynomial Inequalities

This concept involves solving inequalities where a polynomial expression is compared to zero or another expression. The objective is to determine the set of variable values for which the inequality holds by identifying regions in the domain where the polynomial is positive, negative, or zero.

Rearranging to Standard Form

In solving inequalities, a common step is to rearrange the inequality so that one side is zero. This standard form allows for a clearer analysis of the polynomial's behavior and helps in identifying the roots or critical points that separate intervals with different signs.

Finding Zeros of a Polynomial

Finding the zeros, or roots, of a polynomial is crucial because they are the points at which the value of the polynomial equals zero. These critical points divide the real number line into intervals that can then be analyzed to determine where the polynomial meets the inequality condition.

Interval Notation

Interval notation is a method of writing subsets of the real numbers by indicating the endpoints of the intervals and whether these endpoints are included. It is a concise way to express the solution set of an inequality and is commonly used after determining the valid intervals through sign testing.

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