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 - 2x + 1 = 0

Accepted Answer

Welcome back. I'm so glad you're here. We have the equation four X squared minus 28 X plus 49 equals zero. And we're to calculate the discriminate of that equation. Well what is the discriminate? We recall from previous lessons that the discriminative it is B squared minus four A. C. When we have a quadratic equation meaning that it's in the format A X squared plus bx plus C equals zero. And we can identify our A terms. So A in this case would be four RB terms, that would be negative 28 R. C terms here. That would be 49. So we've got our A. B. And C. And hey, does that B squared minus four A. C. Look familiar. Yeah that is the part of the quadratic formula that's underneath the radical. And so what we do is we want to think about, okay if we have something inside the radical that's positive. So if the discriminative discriminative is greater than zero then yeah, we're going to have two real solutions here and then we think about, okay, well what if that discriminate is exactly equal to zero? Well then we're going to have exactly one real solution. And if our discriminate is less than zero. Well then we're going to have no real solutions. We'll have two imaginary solutions but no real solutions. So the discriminate is really helpful in letting us know whether we're going to have two or one or no real solutions. Now we can just go ahead and plug all of this in to our discriminate B squared minus four A. C. So B. That is negative 28 squared minus four times A is four times C, which is 49 -28 Squared. That is 784 and four times four times 49. That is also 784. So we've got 784 minus 784. Hey, that is equal to zero. So that means that there is one real solution to that equation. We look at our answer choices and that matches with answer choice B. Well done, we'll catch on the next one.

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