Problem

Solve each inequality, and graph the solution set…

02:27

Problem 17 Easy Difficulty

Solve each inequality, and graph the solution set.
$$
z^{2}-4 z \geq 0
$$

Answer

$$
(-\infty, 0] \cup[4, \infty)
$$

Related Courses

Precalculus

Algebra

Beginning and Intermediate Algebra

Chapter 11

Quadratic Equations, Inequalities, and Functions

Section 8

Polynomial and Rational Inequalities

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Video Transcript

All right. We have the inequality X squared minus four acts greater than or equal to zero. We want to find all of the values that make this sentence true. To do this, we're gonna have to factor. We're going to treat this like it's a quadratic equation. So if I factor out now, notice we only have two terms here. But if I factor out a common factor of exile, be left with X Times X minus four. It's greater than or equal to zero. So now I have my two factors. The next thing we want to dio is let each factor equal zero. So I let x equal zero and I let X minus four equals zero. And now we have roots. 014 Now, Usually what we want to do is pick a value between these routes. If their value checks, then I know which way my solution sets going. I know it'll be between 014 If it doesn't check, then I know my solution sets toe left zero into the right of four. So, in other words, if I test X equals one, I will get one squared minus four times one one minus four. His negative three negative three is not greater than zero. So therefore, that fails. It doesn't feel it passed the test. So my solution set will not be between 014 That means then that my solution sat has to be to the left of zero. So, in other words, the interval from negative infinity to zero. Now, I wanted to be greater than or equal to zero. So we're going to include the zero. It's part of the solution set, or we're gonna have the interval from four to infinity. When we graft that solution, son. Then we're gonna have zero and everything to the left of zero. We're gonna have four and everything to the right of four. That's how we graft that solution set.

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