![]() Now we have too many equations, we solve them in parallel. So if we're multiplying two things to get 0, it means either 1 equals 0 or the other equals 0. Now we're going to apply the zero product property. And we can do that from our factoring lessons. So this first thing we're gonna do is factor. And this is important here and it will become important again in the probability lessons, okay. The word used in mathematics is the inclusive or which includes the and case. That is not how the word or is used in mathematics. They mean you could do this or that and the implication is that you can't do both. You see sometimes in colloquial language, people use the word or to mean exclusive or. Or it could be that they both equal 0 at the same time. It could be that B equals 0 and A doesn't 0. It could be that A equals 0 and B doesn't. Thus, A equals 0 or B equals 0, includes three cases. Well, what's the distinction I'm drawing here? The mathematical OR is an inclusive or. Keep in mind that the OR that appears in that statement is the mathematical OR. And before we go on, let's think about this statement for a minute. The Zero Product Property says, if A times B equals 0, if a product of two things equals 0. Because once we have a product that equals 0, we can apply this mathematical law, the Zero Product Property. ![]() So very important to get things equal to 0 first. And notice, we'll be doing this so that this product equals 0. We will factor a quadratic to a product of linear binomials. Because we are gonna employ, all those factoring strategies here. So if you haven't seen those lessons, it will be very helpful to watch those before watching this video. The vast majority of quadratic equations you will see on the test can be solved by the factoring methods we discussed in the factoring lessons. The vast majority of quadratic equations you will see on the test will have two solutions and the quadratic coefficient, the coefficient of x squared will equal 1 unless a numerical greatest common factor can be factored out from all three terms. When we're dealing with quadratics is a completely different procedure of equation solving that we follow and that's what we're gonna talk about here. That is exactly the strategy you wanna follow for linear equations, but following that for quadratics is an unmitigated disaster. So before we even begin to talk about how to solve these, let me say, that the strategy that we learn for linear equations, try to get all the x's on one side of the equation, all the constants on the other side of the equation. Most often these equations have two different solutions. In other words, a quadratic expression set equal to zero. A quadratic equation is one of the form a squared plus bx plus c equals zero. You may remember quadratics from our discussions of expression and factoring.
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