how-to-use-the-quadratic-formula-discriminant-regents-nature-of-roots-algebra-honors

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Good day students welcome to mathgotserved.com in this clip were going to going over how to use the quadratic formula the instructions for the example that we're going to be sold inverse follows we are to describe the nature of the roots of the given quadratic equation will going to describe the nature of the roots of the given quadratic equation using the discriminant okay using the discriminant and then we are to solve the equation using the quadratic formula okay then solve or find the roots the roots are the solution to the quadratic equation okay and find the roots or think about it as a solution using the quadratic formula okay alright so be example that we're going to be looking that's today is the quadratic equation 3X square +7 equals negative 2X okay so the first thing we're going to do is you will going to use the discriminant's to describe the nature of the roots will before we start roots are real quick review on what's the discriminant's rule is in determining the nature of the roots okay so recall the discriminant of the component of the quadratic formula be specific it is erratic Okay so discriminant is b squared minus four A C (b^2-4ac)-only represented with Tom the trinomial symbol okay so if you discriminant Delta is Om negative then that means that you going to have to distinct imaginary roots okay only talk about imaginary roots are going to have that I component there not if you are discriminant is zero then you going to have one real roots okay and that is also known as a double root if you discriminant is positive you going to have two distinct roots okay they can be father separated into rational or irrational that depends on if the discriminant is eat perfect square or not okay so let's say that the discriminant is positive and E perfect square give it's a perfect square was going happen is that the Om square root components will become an integer so you going to have a rational result so this case you going to have two distinct real roots that are rational two distinct real rational roots okay now what if you have a scenario where your discriminant is not a perfect square so you discriminant is positive and not a perfect square in that case you going to have to distinct Om real irrational roots okay think about the rational numbers as numbers that you cannot represents as the quotient of two integers for example you have square roots something like this roots to is irrational because the cannot be represented by the quotient of two integers arrive a number that can be represented of a fraction of two integers is a irrational number right so let's give this for cases in mind and let's take a look at the quadratic equation that we doing with happens going to do in order to find the discriminant and uses to this determine the nature of the roots is we need to write down the discriminant equation okay so part one is to find it discriminant three right so our discriminant Delta is b squared minus four A C (b^2-4ac) now we need to find a BNC now one mistake the students make is the filled to put the equation in standard form before Om finding a BNC okay so the give ourselves a nice little caution here place equation in standard form first okay what is the standard form sum up form is a X square plus be X plus C equals zero you basically second equation equal to zero with the terms in descending order of degrees okay so this must be done first before you determing what ABN CR why computer the discriminant and also the solution of the quadratic equation using the quadratic formula right so let's go ahead and carry out how manipulation 3X square +7 equals negative 2X is clearly not in the standard form because of the can see it's not equal to zero to transform it into the standard form we simply add 2X to both sides so this will be equal to zero in there rearranged terms accordingly okay so we have 3X square plus 2X +7 equals zero so this ladies and gentlemen is the standard form that's we're talking about okay the beauty of the standard form is that it enable us to determing what a BNC are so you have this is your a the coefficient of the X square be the coefficient of X and see if you constant so let's go ahead and write that out we have a equals 3B equals two and see equals seven now let's find the discriminant so is read the formula the discriminant is b squared minus four A C (b^2-4ac) the radical components of the Drabek formula the ready can by the car out the substitution you have two square -4×3×7 now one good practice when you finding the discriminant or using the quadratic equation is to use parenthesis now the use of parenthesis it extremely importance went in the of these terms are negative okay you thoroughly see the benefit here because the all positive the whenever you have a negative term you must use parenthesis in order to avoid

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