Using the discriminant to find the number and type of solution. The discriminant of a formula is basically the same exact thing as what’s underneath the square root of the quadratic formula, b² minus 4ac. And when doing this out is it’s going to tell us the type of solutions we’re dealing with. All we have to do is take our numbers plug them into our formula. b is just 10, so b² is 100, minus 4, a is our first term, c is our last term. We have 100 minus 4 times 6 times 4, 4 times 6 is 24, times 4 is 96 so what we actually have is 100 minus 96 which is the same thing as 4.
Our discriminant is a positive number and it is a perfect square so that’s telling us in our quadratic formula what’s underneath the square root is actually 4. We can take the square root of 4 so we’re actually going to be left with plus or minus just a number, our square root is going to disappear leaving us with plus or minus a number, 2 rational solutions.
By using the discriminant we were able to find the type of solutions for this quadratic equation.