Solve each quadratic equation using the zero-factor property. ...

Question

Solve each quadratic equation using the zero-factor property. See Example 5. x² - 100 = 0

Accepted Answer

Welcome back everyone in this problem, we want to use the zero factor property to solve the quadratic equation M squared minus 256 equals zero for M in our answer choices, A is negative 16, B is negative 18, C is negative six and eight and D is negative 16 and 16. Now, what are we, what are we trying to do here? What do we already know? Well, we want to solve the quadratic equation and to solve it, we need the zero factor property. Now recall that the zero factor property says that if we have two values A and B that are real numbers, so A and B are real numbers and a multiplied by B equals zero, then either A equals zero B equals zero or both A and B equals zero. And that makes sense, right? Because if you're multiplying two numbers and you get 01 of them has to be zero. So what we're trying to do here if we can rewrite our quadratic equation as a product in the same way that A B is a product, then we can set it to zero and solve for one of them because that tells us one of the linear expressions, one of the terms must be equal to zero. So let's go ahead and try that. So we're working with M squared minus equals zero. No, doesn't this quadratic equation look a little interesting. Haven't you seen it before, doesn't it? Or, or don't you notice that M squared is a squared number and 256 is also a squared number and they're subtracting each other. So this represents the difference of two squares. Recall that the difference of two squares tells us that if we have two square numbers and one is subtracting the other or, or we have their difference, then they'd be equal to the product of their sum and difference of the roots of those square numbers. So if we know what the square root of M squared is and the square of 256 is, we can use this property to help us rewrite it as the product of tool linear expressions. And we know that that is because M squared is literally M squared, right? That, that it's squaring M and 256 is the square of 16. So if I write it like this, no, I can put it as the difference of two squares, which would have been M plus 16, multiplied by M minus 16. And that all equals zero. Now, since both of them equal zero, here's where our zero factor property comes in because no, that tells us that either M plus 16 equals zero or M minus 16 equals zero. And if M plus 16 equals zero, then M equals negative 16. Likewise, if M minus 16 equals zero, then M equals positive 16. So those could be the two possible solutions for our quadratic equation. Let's test it out just to make sure that we're correct. So if M plus 16 is our solution, then sorry, if me equals negative 16, my bad, then if I put it in my equation, that would be negative 16 squared. So this is our test. So negative 16 squared minus 256 equals zero. We're testing if that is true. Now, negative 16 squared is negative 16 multiplied by negative 16. And that's a positive 256 and 256 minus 256 does indeed equal zero. If we test it with MB and equal to 16, then that means we'd have 16 squared minus equals zero and 16 squared is 256 minus 256 does indeed equal zero. Therefore, our possible answers could have been M equals negative or M equals 16. And when we go back to our solutions or that would have been answer choice. D Thanks a lot for watching everyone. I hope this video helped.

Solve each quadratic equation using the zero-factor property. See Example 5. x² - 100 = 0

Key Concepts

Zero-Factor Property

Factoring Quadratic Equations

Difference of Squares

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