Solve each polynomial inequality in Exercises 1–42 and graph the ...

Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x^2≤2x+2

Accepted Answer

Solve the following polynomial inequality X squared less than equal to eight X plus six. I've got to be right. This just a little bit. I want my eight X with the X squared sauce. In fact checks on both sides to get X squared minus eight X less than equal six. Now I'm going to complete the square so it could be the square. We take the term on our X divided by two and square. It says 8/2 squared, which is 16, We're gonna add 16 to both sides. Now X squared minus eight X plus 16, not equals but less than equal to six plus 16. This on the left factors, two x -4 squared On the right, we skipped 22. Now say the square above sets, get rid of the square. We will now split this up. We have X -4, Less than equal to the square of 22 and greater than equal to the square of negative, negative square of 22. Like so because we took the square root, we have two different answers. So now we have our interval, our interval Is Square 22 greater than X -4 square than -22. We actually want to do one more thing and add our forward about sets. So actually weren't quite done yet, but now we are plus four, less than equal to X equal to square of 22 plus four by adding four to both sets. So our X is between these two values, which means we want close bracket, negative square 22 plus four and square of plus four. Like so, or whether you write it 4 - And four plus square, the 22. Now, we want to look at our possible answers. Well, if you look over here, answer A is not correct because we have the wrong brackets. Answer C and D have squared of 10 instead of the square root of 22. This means the answer to our problem turns out to be answer B okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x^2≤2x+2

Key Concepts

Polynomial Inequalities

Graphing on a Number Line

Interval Notation

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