hello I make them to the nation's to your channel so today we are going to discuss about felonies Manta that means how we can solve a by quadratic equation having degree 4 so the basic point now after this process in this process is that you need to reduce the degree of your equation that means you have by quadratic equation having degree 4 reduce it transform it into cubic and then quadratic and now after you know how to solve a quadratic equation either by using quadratic margin or splitting the term method okay one more trick which you need to use here is that you need to consider another by quadratic equation of the form let's see of the form X square plus half of this coefficient so half of 2 is 1 X plus lambda whole square now because you have to do this which can they expand it as you can see this is your part now you can apply a plus B plus C whole square here so a square plus B square plus C square plus 2 a B plus 2 BC plus 2 C ok so what you are observing here is that this is having only two terms from the question right so all the other terms are extra so you need to remove all other terms so minus X square minus lambda square plus 2 X lambda minus 2 lambda X square and rest of the question should be written here minus 5 X 5 plus 10 X minus 3 equals u all right now dig all of the downs apart from this by quadratic equation on the right inside X y plus lambda square minus 2 it's lambda plus 2 lambda x squared plus 5x squared minus 10x plus 3 okay now collect all the like terms all together so first of all hi nice power X square so it is 1 then 2 lambda this is v 1 plus 5 is 6 plus 2 lambda then after X so coefficient of x here is minus 2 lambda minus 10 and the constant term and the last okay now you can see that this right-hand side is we have right-hand side equal to a perfect square right and perfect square no like 480 for example 81 you have perfect square as none now that means you have equal roots real and equal roots for this so if you have real n equal roots for a quadratic equation that means when you will apply one big formula you will have your discriminant as 0 that's correct so D should be 0 that means b square minus 4ac should be 0 that means B Square should be Boise all right now the coefficient of x 1 is a this is B this is C what do you have on the values here so minus 2 lambda minus 10 whole square is equal to 4 e see if you take minus 2 common so 2 square for lambda plus 5 and if you expand this 6 lambda square 6 times 3 is 18 2 lambda Q the 6 lambda so 4 is Kassovitz for now open this as well so what it would be a square plus B square plus 2 in right now so this for lambda okay solve this for lambda let me grab just so you can see how this is how to lambda cube this is your six lambda square and this is lambda square in negative so plus 5 lambda square you have done with this then after this is fixed on dock 6 minus 10 is for aging minus 25 s 7 right now because this is a cubic equation so you will have 3 roots for this but you need to find one of the root which should be in the most simplified form now if you see my hated trial we can see let's say if we will put lambda as minus 1 so minus 2 plus 5 plus 4 minus 7 so 9 minus 9 is 0 so that means lambda minus 1 is like wish'd is the root for this equation so what lambda minus 1 into your main equation this one if you will put lambda minus 1 here what you get see let me use this lambda is minus 1 so XY minus X plus lambda whole square which is minus 1 it would be X well 6 minus 2 is 4 and this is minus this is minus 1 minus minus plus minus 8x minus 1 is this so full right so you can write it as see if you write it as take fold on it what is left now this is the square for X minus 1 whole square right now you can think of various ways like cancel this 2 with this 2 if you can write it as 2 square but don't do this because then you will get only two roots however because this is a bi quadratic equation and it's decreased for that's what you should have for roots right so what you can do see I can write it as if I take to insight 2x minus 2 whole square right and if you bring this into the left hand side you can see that this is forming the form of a square minus B Square right so is y minus B Square is what that's correct a plus B Y is this minus B so minus 2x plus C right so now you can see initially we meet quite cubic equation now we have two quadratic equation so simplify this X square to x16 is X minus 3 and here minus 3x plus 1 now you can see you can put this as 0 this as 0 that means you are having two-part equation now I Plast either splitting the tomate quadratic formula so from this x squared plus you want - real light so what you can do plus 3x - X and for this X square again what how he can write it because you need one so for this you can apply a quantity formula right this is your minus 3x plus 1 yes so apply quantity formula for this what is a 1 B is minus DS is 1 so DS equals to b square minus 4ac which is 5 so this is root 5 square so you exhale B minus B which will be which will be in plus 3 plus minus root D so root will be canceled square by 2 it so these are your two roots and from here X plus 3 minus 1 X plus 3 so from here you will get to equation 2 2 roots as minus 3 and 1 so these are your C 3 plus root 5 by 2 3 minus root 5 value these are your four roots for this particular pie quadratic equation alright I hope you understand this video fully and if so then don't forget to Like share and subscribe my channel till my next video take care of yourself bye bye