Visit: http://academyofone.org courses: http://www.academyofone.org/courses Royalty free music licensed by http://www.stockmusic.net Royalty free photos licensed by http://www.bigstockphoto.com Script: In the last video we talked about quadratics. After learning about those little things we talked about solving quadratics with factoring. That’s cool and all but we can solve quadratics other ways. What’s going on everybody! My name is Jack Jenkins and this is Academy of One. Today we are talking about the square root property. When we solve quadratics by factoring it helps that we have a first-degree polynomial or we have the quadratic equal to zero. If neither of these are the case then don’t factor and use this method instead. The square root method is pretty simple. a squared equals b, where a equals a mathematical expression and b is a nonzero number. This little property tells us a lot. So if a squared equals b then a equals positive or negative square root of b. This plus or minus sign will tell us that there are two answers in this problem. One solution will be positive as noted by the plus sign and one solution will be negative as noted by the minus sign. I’m going to tell you now that the answer to these problems may look messy and complicated. More often then not we will have an imaginary number in our answer. All right, just telling you what it is and how complicated it’ll look isn't going to help you a whole lot. Let’s go ahead and do some example problems. As tradition I will do one problem and you will do the next. Let’s rock! The first one I’m going to do is nine x squared plus twenty-five equals zero. Now look at this form and now look at the square root property. Notice the difference? We have that ugly looking non-variable term there. Man we need to get this ugly goose outta here. What we do to get rid of it is subtract it from both sides. The problem is now nine x squared plus twenty-five minus twenty-five equals zero minus twenty-five. Simplify the expression and you’ll get nine x squared equals negative twenty-five. Now we need to isolate the x value by dividing nine from both sides. The problem is now nine divided by nine x squared equals negative twenty-five divided by nine. Combine those like terms to get x squared equals negative twenty-five over nine. Now let’s bring up that square root property form and... yep they look alike now! Let’s apply that property to this hideous quadratic. We have x equals negative or positive the square root of negative twenty-five over nine. Oh... well we have a square root of a negative number! You know what that means right? We have to switch out the negative sign for an i. The problem is now x equals plus or minus i times the square root of twenty five over nine. Now let’s simplify the square root by applying it to both the numerator and the denominator. The square root of twenty-five is five and the square root of nine is three. The final form of this solved quadratic is x equals positive or negative five over three i. We can also say it as x equals five over three i and x equals negative five over three i but that takes more time to say. This solution may look messy but this is actually the answer. We can check our answer to see it’s correct. Nine times positive or negative five over three i in parenthesis squared plus twenty-five equals zero. The reason why I put the positive or negative form of the answer together is because this is a quadratic. Squaring a positive answer gives us a positive form and squaring a negative answer gives us a positive form. It’s ok to check both forms of the answer because it’s literally the same thing. Thanks square for making my life easier. Now let’s solve this puppy out. The first thing to do is distribute the square on to our positive or negative five over three i. The whole quadratic is now nine times twenty five over nine i squared in parenthesis plus twenty-five equals zero. Remember young ones, pemdas so the first thing we need to do is solve out the square of i. As we talked about in the last unit, i squared is equal to negative one so the problem is now nine times twenty-five over nine times negative one plus twenty-five equals zero. Simplify the parenthesis to get nine times negative twenty-five over nine in parenthesis plus twenty-five equals zero. The nine outside the parenthesis and the nine in the denominator of the fraction will cancel out giving us this beautiful negative twenty-five. All hail the negative twenty-five. The problem is now negative twenty-five plus twenty-five equals zero. Negative twenty-five plus twenty-five is equal to zero and zero is equal to zero so the problem is done. The answer to nine x squared plus twenty-five equals zero is positive or negative five over three i. Man this was such a large problem but that’s what you get when you solve those quadratics. And of course here is the graph of this quadratic. Such a beautiful graph.

• published: 07 Apr 2015
• views: 5