In Exercises 75–82, compute the discriminant. Then determine the ...

Question

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation.

x^2 - 3x - 7 = 0

Accepted Answer

Welcome back. I'm so glad you're here. We've got this equation, we have X squared minus 11. X minus 12 equals zero. And we are asked to calculate the discriminative. It well what is the discriminative? We recall from previous lessons that the discriminate is B squared minus four A. C. When we have a quadratic equation in the form A X squared plus bx plus C equals zero. And we can identify our A. B and C terms in this case A equals one, B equals negative 11 and C equals negative 12. And then the discriminate tells us when we plug in for R A B and C terms. It tells us some really important information about how many solutions we have. And that's because that B squared minus four A. C. That's really familiar. Yeah, that is from the radical of the quadratic formula. So when we've got something inside a radical, well if it's a positive, if D is greater than zero then you're going to have two real solutions because you're going to take the plus or minus of what's in that radical. But if D equals exactly zero. Well then you're going to have one real solution Because plus or zero is just going to be plus and zero. And then if you've got d is less than zero, you've got a negative number inside that radical, you're going to have no real solutions. You'll probably have two imaginary solutions but no real ones. So the discriminate is great for helping us figure out that information and now we can go ahead and plug in to our B squared minus four. A. C B is negative 11. So we've got negative 11 squared minus four times A is one times C is negative 12 negative 11 square. That's 121 negative four times one is negative four times negative. 12 is going to be positive. 48 121 plus 48. That's 169. 169 is greater than zero. So that means there will be two real solutions. We look at our answer choices and that matches with answer choice. A well done, we'll catch you on the next one.

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