Factoring Using the Discriminant

Hi, I'm Rachel and today's topic that we are discussing is factoring using the discriminant. Well the discriminant is the part of a quadratic equation that is in the square root. It is B squared minus 4AC. If you remember the quadratic equation, negative B plus or minus the square root of B square minus 4AC all over 2A, it's that part that's in the square root there. So, this is our discriminant. Well this isn't going to tell you the answer exactly but it is going to tell you the amount of solutions you have. What does that mean? That means if D, this discriminant here, is greater than 0, you are going to have two real solutions. If D is less than 0, you are going to have two imaginary solutions and if D equals 0, you are going to have one real solution. So what does that mean? Why is this? This is because if you think about it, if a positive number is in a square root, you get two real answers right? You have both a positive and the negative and they are both real numbers, but if you have a negative number in a square root, you are going to get an imaginary number because there is no real number that you can get when you square root a negative number right? The square root of negative 2, that's going to be a non-real solution, it's going to be imaginary, but there will be two conjugate pairs of that. When you have D equals 0, you are going to have one real solution, right? If there is just one number here, there is going to be one solution, the square root of 0 is always going to be 0. There's always going to be, there is no positive or negative 0 right, it's just one, just one 0. So that's why you will have one solution and that is using the discriminant to solve for this quadratic equation and using it to see how many solutions you will have. I am Rachel and thank you for learning with me today.