what is the discriminant of the quadratic equation 2x + 5×2 = 1? –18 –16 22 24 This is a topic that many people are looking for. amritsang.org is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, amritsang.org would like to introduce to you What is the discriminant and what does it mean. Following along are instructions in the video below:
So when were looking at what is the discriminant. The discriminant is going to to help us determine what type of solutions. We have for a quadratic equation or so remember when we first learned about racking there we turned out there was three different types of solutions.
We can well just kind of drop three little for a quadratic equation. We know that shape takes a parabola. So we could have an equation like the paragraph.
Where theres exactly one x intercept. We could have one where theres no x intercepts. And we also have one where theres two x intercepts.
All right so we could have one nine for two so what were going to do is were gonna use the discriminant. Applying the quadratic form. Its very helpful you can understand what types of solutions.
Youre gonna have so. When we look at this quadratic formula x. Equals opposite of b.
Plus. Or minus. The square root of b.
Squared. Minus four times a times c all over 2a. This is the big kind of formula right and not always when you look at this when youre plugging in numbers.
Youre going to say. Well you can sometimes find that you know the x intercepts. But a lot of times.
Its very helpful to kind of know what should you expect to make sure youre doing your math correctly you know and were a lot of times will say you know what type of solutions is a graph where we dont even have to go through the whole formula. We can just be able to determine their scrutiny. So.
The discriminant is very simple all it means is b. Squared minus 4. Times a times c.
And what you can see is the discriminant is what is under the square root all right so theres a couple different types of solutions. Were going to get determining what our what our discriminant is all right so our discriminant is right on our square root.
So now we need to think about well what types of numbers can we take the square root of so in our discriminant and we can 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. 80. 100.
120. 1. Forty.
Four. 169. Dot.
Dot. Dot. Dot.
Dot. Dot. We can keep on going up.
As long as were taking the square root of that number what were going to have is were gonna have a rational number right because the square root of 25 is positive the plus or minus five right so. Were gonna have two integers so if its a square number. Then we can have two what we call two real rational roots.
However. Lets pretend we have the square root of eight now the square root of eight is not a rational number thats an irrational. So if i have the square root of eight then im going to have two real.
Its still gonna be a real number. But its going to be irrational roots and lets call this permanent.
So lets call it d. So if i have d is a square number okay. Lets do d.
So d is positive and a square number. Then i have two real rational roots. If d is positive and a non square.
Number not square numbers would be all the numbers that are not squared like 8 7. 11. 15.
Then were going to have two real irrational roots and just remember to be rational means that the numbers is gonna repeat infinity and lets say what about if we have the number zero well you cant take the square root of zero. And ive taken a plus or a minus right. We know that the square root of 25 can be 5 squared or negative.
5 squared. But the square root of zero is zero doesnt have a positive or negative side so you cant say zero squared and negative zero square because zero doesnt have a positive or negative attea attached to it so therefore if we have zero. Now what were gonna have is just sorry.
Were going to have one real rational. All right. And you can see the example four zero would be up here.
Where were gonna only have one real rational roof. These first two would be examples here. Where you have your x intercept be in rational numbers they can be like negative.
5. And positive. 5 or they could be like this could be like negative 2 square.
Root of 3 and positive the square root of three where theyre irrational. But theyre still going to be two different roots and then what about if we have our discriminant is negative. It doesnt matter if its a negative square.
Number. A negative irrational number. As long as its negative.
Youre not going to have any x intercepts. So therefore. We say youre going to add two complex 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 you .
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