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Zero Product Property - Definition and Examples - What is the Zero Product Property (AKA) Zero Product Principle? 

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What is zero product property. Zero Product Property - Definition & Examples - Expii

  The Zero Product Property simply states that if ab = 0, then either a = 0 or b = 0 (or both). A product of factors is zero if and only if one or more of the. Zero product property defines that if A and B are two real numbers and multiplication of A and B is zero then it must be either A=0 or B=0 and there might be.  

Zero Product Property.Zero Product Property - Definition, Formula, Examples

 

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Next lesson. Current timeTotal duration Google Classroom Facebook Twitter. Video transcript - [Instructor] Let's say that we've got the equation two X minus one times X plus four is equal to zero.

Pause this video and see if you can figure out the X values that would satisfy this equation, essentially our solutions to this equation. Alright, now let's work through this together.

So at first, you might be tempted to multiply these things out, or there's multiple ways that you might have tried to approach it, but the key realization here is that you have two things being multiplied, and it's being equal to zero. So you have the first thing being multiplied is two X minus one. This is expression is being multiplied by X plus four, and to get it to be equal to zero, one or both of these expressions needs to be equal to zero. Let me really reinforce that idea.

Well, can you get the product of two numbers to equal zero without at least one of them being equal to zero? And the simple answer is no.

If A is seven, the only way that you would get zero is if B is zero, or if B was five, the only way to get zero is if A is zero. So you see from this example, either, let me write this down, either A or B or both, 'cause zero times zero is zero, or both must be zero. The only way that you get the product of two quantities, and you get zero, is if one or both of them is equal to zero.

I really wanna reinforce this idea. I'm gonna put a red box around it so that it really gets stuck in your brain, and I want you to think about why that is. Try to come up with two numbers. Try to multiply them so that you get zero, and you're gonna see that one of those numbers is going to need to be zero. So we're gonna use this idea right over here.

Now this might look a little bit different, but you could view two X minus one as our A, and you could view X plus four as our B. So either two X minus one needs to be equal to zero, or X plus four needs to be equal to zero, or both of them needs to be equal to zero.

So I could write that as two X minus one needs to be equal to zero, or X plus four, or X, let me do that orange. Actually, let me do the two X minus one in that yellow color.

So either two X minus one is equal to zero, or X plus four is equal to zero. X plus four is equal to zero, and so let's solve each of these.

If two X minus one could be equal to zero, well, let's see, you could add one to both sides, and we get two X is equal to one. Divide both sides by two, and this just straightforward solving a linear equation. This is interesting 'cause we're gonna have two solutions here, or over here, if we wanna solve for X, we can subtract four from both sides, and we would get X is equal to negative four. So it's neat. In an equation like this, you can actually have two solutions.

I think it's pretty interesting to substitute either one of these in. And so what's this going to be equal to? One minus one is zero, so I don't care what you have over here. Zero times anything is going to be equal to zero.

And likewise, if X equals negative four, it's pretty clear that this second expression is going to be zero, and even though this first expression isn't going to be zero in that case, anything times zero is going to be zero.

Let's do one more example here. So let me delete out everything that I just wrote here, and so I'm gonna involve a function. So let's say someone told you that F of X is equal to X minus five, times five X, plus two, and someone said, "Find the zeros of F of X. When does F of X equal zero? For what X values does F of X equal zero? That's what people are really asking when they say, "Find the zeros of F of X.

Well, F of X is equal to zero when this expression right over here is equal to zero, and so it sets up just like the equation we just saw. X minus five times five X plus two, when does that equal zero? And like we saw before, well, this is just like what we saw before, and I encourage you to pause the video, and try to work it out on your own. So there's two situations where this could happen, where either the first expression equals zero, or the second expression, or maybe in some cases, you'll have a situation where both expressions equal zero.

So we could say either X minus five is equal to zero, or five X plus two is equal to zero. I'll write an, or, right over here. Now if we solve for X, you add five to both sides of this equation. You get X is equal to five. Here, let's see. To solve for X, you could subtract two from both sides. So here are two zeros.

You input either one of these into F of X. If you input X equals five, if you take F of five, if you try to evaluate F of five, then this first expression's gonna be zero, and so a product of zero and something else, it doesn't matter that this is gonna be The second expression right over here is gonna be zero. Zero times anything is zero. Up Next.

   

 

What is zero product property -

    Dec 04,  · A non-example of a product is where it equals 0. This is called zero-product property. This is the property of two non-zero elements being zero. In chemistry, it would be any substance which is a reactant. The zero product property, also known as the zero product principle, states that if p is 0 or q is 0, then either p is 0 or q is 0 or both p is 0 and q is 0. For example, x2 = 6x 5 = 0 or (x 1) (x 5) = 0. How is this useful? identify the search term you are interested in (i.e. zero product property calculator) in the leftmost column below. Click on the appropriate program demo found in the same line as your search phrase. If you find the software demo useful click on the purchase button to obtain the program at a special low price offered to.