Write a quadratic equation in general form whose solution set is ...

Question

Write a quadratic equation in general form whose solution set is {- 3, 5}.

Accepted Answer

Welcome back. I'm so glad you're here. We are given a solution set of two negative one. What does that mean? That means that X equals two and X equals negative one. And we are to write a quadratic equation in general form. What is that? That will give us an equation that looks like a X squared plus bx plus C equals zero. Okay. How do we get from the one to the other? Well we know that when we have something equal to zero we just need factors where either one of them equals zero and that will get it to equal zero on the right hand side. And we know that we could set both of these two. X equals two and X equals to one equations equal to zero. So let's bring that to over to the left hand side will subtract it from both sides. So we have x minus two equals zero. There's one of our zeros and we also know we can add one to both sides here and that would give us an X plus one equals zero. So we can take both of these two expressions on the left hand side of the equation and we can plug those in to our parentheses because we know that those equal zero. And when you have something that multiplies and 10 then the right hand side will equal zero. Okay, so let's put these in parentheses. Now we have x minus two Times X-plus one equals zero. Now to get that looking like general form we just need to foil that out. So our first X times X is X squared. Our Outsides X times one is plus one X. Our insides negative two times X is a minus two X. And our last negative two times one is going to be minus two. All equal zero. Let's combine our like terms in the middle here we'll have X squared one X minus two. X is a minus one, X or minus X minus two equals zero. And that is in the correct general form of a quadratic equation. We look at our answer choices in this matches with answer choice C. Well done, we'll catch you on the next one.

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