okay so when we're looking at what is the discriminant the discriminant is going to help us determine what type of solutions we have for our quadratic um equation or function so remember when we first learned about graphing there's we turned out there was three different types of solutions we can have I'll just kind of draw three little graphs here okay for a quadratic equation we know that sh a parabola so we could have an equation like the parent graph where there's exactly one x intercept we could have one where there's no x intercept and we can also have one where there's two x intercepts all right so we could have one none or two so what we're going to do is we're going to use the discriminant because when applying the quadratic form it's very helpful to kind of understand what types of solutions you're going to have so when we look at this quadratic formula X = opposite of B plus orus < TK of b^2 - 4 * a * C all over 2 a this is a big kind of formula right and not always when you look at this when you're plugging in numbers you're going to say well you can sometimes find the you know the X intercepts but a lot of times it's very helpful to kind of know what should you expect to make sure you're doing your math correctly and and a lot of times we'll just say you know what type of solutions does a graph have where we don't even have to go through the whole formula we can just be able to determine the discriminant so the discriminant is very simple all it means is B ^2 - 4 * a * C and what you can see is the discriminant is what is under the square root all right so there's a couple different types of solutions we're going to get determining what our what our discriminant is all right so our discriminant is right under our square root so now we need to think about well what types of numbers can we take the square root of so if our discriminant if we take the square root of the number that means we have a square number square numbers such as 1 4 9 16 25 36 49 64 81 100 121 144 169 um dot dot dot dot dot dot dot we can keep on going up as long as we're taking the square root of that number what we're going to have is we're going to have a rational number right because the square of 25 is positive a plus or minus five right so we're going to have two integers so if it's a square number then we can have two what we call two real rational Roots however let's pretend we have the square root of eight now the square root of eight is not a rational number that's the irrational number so if I have the square root of eight then I'm going to have two real it's still going to be a real number but it's going to be irrational Roots um and let's call the discriminate so let's call it D so if I have D is a square number uh let see here okay let's do D so if D is positive and a square number then I have two real rational Roots if D is positive and a non square number non square numbers all the numbers that are not squared like 8 7 11 15 then we're going to have two real irrational roots and just remember irrational means that the number is just going to repeat Infinity um and let's say what about if we have the number zero well you can't take the square root of zero and obtain a plus or a minus right we know that the square of 25 could be 5 S or negative 5 squ but the square of z0 doesn't have a posit for negative side so you can't say it's 0qu and negative 0 S because zero doesn't have um a uh a positive or negativity attached to it so therefore if we have zero then what we're going to have is just uh sorry we're going to have one real rational root all right and you can see in an example for zero would be up here where we're going to only have one real rational root these first two would be examples here where you could have your x intercept being rational numbers they could be like5 and positive five um or they could be like uh this could be like um negative the square root of three and positive the of three where they're irrational but they're still going to be two different roots and then what about if we have our discriminant is negative it doesn't matter if it's a negative square number a negative irrational number as long as it's negative you're going to have any um x intercept so therefore we say you're going to have two complex Roots so there you go ladies and gentlemen that is an example of what the discriminant is and what it tells us about our solution thanks