Hey, everyone. As you solve quadratic equations using the square root property, you may end up getting an imaginary or a complex root. But that's totally fine because we know how to deal with complex numbers, and we're just going to simplify it as we would any complex number. So let's look at an example. Here we have x2+4 plus 25 is equal to 0. And I want to solve this using the square root property. So starting with step 1, of course, I want to isolate my squared expression. Now my squared expression is just this x2 so I want to go ahead and get that by itself by first moving this 25 over, and I can do that by just subtracting 25 from both sides. I'm left with 4x2=-25 and then divide by 4 to get that x2 by itself. I am left with x2=-254. So step 1 is done. I have isolated my squared expression and now I want to take the positive and negative square root. So taking the square root of both sides here it will cancel on this side. I'm left with x=±-25/42. Now I can go ahead and simplify this further and I can separate it out into ±-254 just using my radical rules. Now I have a negative under the square root here but it's totally fine because we've seen this before and we know how to deal with it. So let's go ahead and simplify this. Now this square root of negative 25 is just going to become 5 I and then we know that the square root of 4 is just 2. So really, this simplifies all the way into ±5i2. So we have completed step 2. We've taken our positive and negative square root, and x is actually already by itself so step 3 is done as well. And now I just have my solution. So my solution is x=±5i2. And I can, of course, separate these into the positive and negative if I want as well. Now whenever you're dealing with a complex answer, it's totally fine. It's fine to have the imaginary unit. And a clue that you might end up with a complex answer is if in your standard form equation a and c have the same sign, then you're always going to end up with a complex answer. That's all there is for imaginary roots. I'll see you in the next video.
- 0. Fundamental Concepts of Algebra3h 29m
- 1. Equations and Inequalities3h 27m
- 2. Graphs1h 43m
- 3. Functions & Graphs2h 17m
- 4. Polynomial Functions1h 54m
- 5. Rational Functions1h 23m
- 6. Exponential and Logarithmic Functions2h 28m
- 7. Measuring Angles39m
- 8. Trigonometric Functions on Right Triangles2h 5m
- 9. Unit Circle1h 19m
- 10. Graphing Trigonometric Functions1h 19m
- 11. Inverse Trigonometric Functions and Basic Trig Equations1h 41m
- 12. Trigonometric Identities 2h 34m
- 13. Non-Right Triangles1h 38m
- 14. Vectors2h 25m
- 15. Polar Equations2h 5m
- 16. Parametric Equations1h 6m
- 17. Graphing Complex Numbers1h 7m
- 18. Systems of Equations and Matrices1h 6m
- 19. Conic Sections2h 36m
- 20. Sequences, Series & Induction1h 15m
- 21. Combinatorics and Probability1h 45m
- 22. Limits & Continuity1h 49m
- 23. Intro to Derivatives & Area Under the Curve2h 9m
1. Equations and Inequalities
The Square Root Property
Video duration:
2mPlay a video: