Using the discriminant to find the number and type of solutions. The discriminant is the part of the quadratic formula that is underneath the square root, which is b² minus 4ac and basically by using this we’ll be able to figure out the number and type of solutions. We won’t know what our solutions are but we’ll know the general look or feel of what they’re going to give us.
All we have to do is take our quadratic equation and plug it into our formula. So b², b is -4, negative 4² is 16 minus 4, a is our first term which is 5 and c is our last term which is -3. So 16, we’re minusing, this is going to be negative so it’s going to turn positive, 4 times 5 is 20, times 3 is 60. 16 plus 60 is 76. So our is positive but it’s not a perfect square which means when we take the square root of it we’re going to be left with a square root which tells us that we are going to have two answers. We have the plus and minus the square root. So we have two answers, we’re going to have the square root so they’re going to be irrational.
By using the discriminant we were able to figure the type and number of our solutions to a quadratic equation.