 Hello friends, welcome to this new session on quadratic equation and in the following few lectures we are going to cover the topic quadratic equation. We will understand the importance of this particular algebra topic as a very important tool to understand different mathematical problems and this tool is used not only in mathematics but you will see this is very very useful in other areas of science for example physics, chemistry and likes of that. So hence it is very important that we must have very thorough understanding of quadratic equation. Where do we use quadratic equation? What are the application areas of quadratic equation? What are different properties and you know related to quadratic equations and things like that. So let's begin in how we are going to approach this topic is like we have been doing so far. So we will be giving you lectures and then post that lectures there will be few solved examples and after the solved examples you need to solve unsolved examples and then try them out and you know obviously now mathematics as you know requires a lot of practicing. So hence only by viewing this lecture it will not be sufficient. So after you view the video what I would suggest is go through the solved examples first and then try to solve unsolved examples and you can reduce the pace of the lecture as well to understand the concepts. So my request to all of you would be to have a very thorough understanding of this topic because it's going to be very very vital tool in your future endeavours related to science education. Now so what is quadratic equation and why is quadratic equation called quadratic equation? So if you see if I break this word and if I try to understand the root word the root word is quad. Now quad is a Latin word okay guys Latin is you know the language you know used by Greeks. So in Latin quad comes from the from other word called quadratus okay which word quadratus and quadratus in Latin means a square a square. So in quadratic equation actually we deal with with expressions which has power or degree maximum degree as 2 so hence and we know that those kind of expressions are called quadratic expressions are polynomials so hence the word quadratic equation right. So square because if you have already learned it or most of you would have known that quadratic equation R of the form of a x square plus b x plus c equals 0 is it it. So hence if you see the degree here is clearly 2 the degree of the polynomial in the left hand side is 2 which we usually call as square term and hence the word quadratic okay. So let us now begin with the understanding of quadratic equation. Now the second part of this term is equation. So what is an equation guys. So if you see equation is nothing but if you have an expression expression 1 when equated to expression 2 expression 2 it becomes an equation right this is an equation. Now you would ask what is what is an expression basically. Now we have already learned there are different types of expression or if you don't know let me tell you the expressions could be of algebraic expression. So you have algebraic expression so for example 3x square minus 2 is equal to 4x plus 5. So if you see there is an algebraic expression in LHS and an algebraic expression in the RHS which are equated with this equal to sign and hence this is called algebraic equation. Similarly I can have a trigonometric equation how so you have to have trigonometric expressions in both sides. So if you write sin theta is equal to 2 cos theta then it becomes a trigonometric equation right. Similarly that could be something called exponential equation exponential equation how so 2 to the power x let's say is equal to 3 to the power y into 4 to the power let's say z. So this is an exponential equation and likewise we have something called logarithmic logarithmic equation. So a natural log of 2x plus 3 is equal to let's say 4 is a logarithmic equation right. So hence you can have combination of expressions as well. So algebraic equated to trigonometric or to exponential and likewise correct. So this is what is called an equation. So what is quadratic equation in that case so when so hence this is quadratic equation what is quadratic equation. So quadratic equation first of all first of all is a is an algebraic equation. So the first one which we are discussing here algebraic right algebraic equation now what kind of algebraic equations basically if you take px and equate it to let's say 0 okay where px is a quadratic quadratic polynomial quadratic polynomial right then you will get what a quadratic equation. Now you can ask okay is it necessary to equate it to 0 not necessary. So you can equate it to either 0 or a linear term linear expression let's say linear polynomial let me write linear polynomial linear polynomial or you can equate it to a quadratic polynomial as well quadratic polynomial as well but you have to make sure that then after you equate it to a quadratic polynomial the coefficient of x square must not be 0. So you have to make sure that coefficient of x square cannot be 0 under any circumstances we'll see why okay. So this is what quadratic equation would look like. So for example let's say px let us say px is 3x square minus 2x plus root 2 okay so this is a quadratic polynomial now equate it to any gx such that gx is either of a polynomial polynomial polynomial of degree 0 1 or 2 right and when it is a degree of degree 2 we must ensure that the coefficient of x square after simplifying should not be 0 what do I mean by that is simply this. So let us say px is let it be same as the given px and let's say gx is 3x square minus 2. So when you equate px equals to gx what will happen px equals to gx is equal to 3x square minus 2x plus root 2 is equal to 3x square minus 2. So in this case if you see 3x square and 3x square will just get cancelled out which is not allowed so hence you can't equate a px to another quadratic gx such that the the coefficient of x square gets eliminated. However let's say if gx was let's say 2x square minus 2 then you can do this then you can equate px into gx so hence I can write now 3x square minus 2x plus root 2 equals 2x square minus 2 so this is definitely a quadratic equation right. So gx can also be simply 0 so equate the equate px to 0 then it will be a quadratic equation gx could be another constant let's say 5 or root 2 or minus root 7 whatever then again you will get px equals to gx as a quadratic and gx could be let's say x plus 1, 2x minus 1 and all that right linear terms degree 1 then also you can get a quadratic equation what do I mean so let us say let us try these 1, 2 and 3 so in the first case you will get 3x square minus 2x plus root 2 which was px which we have chosen equals to 0 this is first quadratic equation okay quadratic equation number one you got then 3x square minus 2x plus root 2 equals to 5 it's another quadratic equation right and similarly 3x square minus 2x plus root 2 is equal to x plus 1 is another quadratic equation okay so in every case you'll see you can you this can be reduced to simply 3x square minus 2x plus root 2 equals to 0 then this can be reduced to 3x square minus 2x plus root 2 minus 5 equals 0 and this can be expressed as 3x square minus 2x now in fact this will be minus 3x now so this x will come here and get added to this so minus 3x plus root 2 minus 1 equals to 0 so in if you if you now try to see a trend so we have x square that is variable square and then there is a coefficient here a correct then there is an x here and then there is a coefficient b and then finally a term which is having no variable I can call it as c and this is equated to 0 so all the quadratic all the equations of this form where a shouldn't be 0 a shouldn't be 0 and a b and c are real numbers real numbers then we say what do we say this type of equation will be called as quadratic quadratic equation I hope you understood so hence please bear this in mind you should actually write it somewhere as well so at a square plus b square a square x plus b x plus c equals to 0 a not equals to 0 and a b c are real numbers such type of equations will be called quadratic equations so examples let us take examples we have already taken so examples would be 2x square minus 3x plus 9 equals 0 root 7x square minus 14x plus 21 equals to 0 root 3 plus 1x square minus root 3 minus 1x plus 4 is equal to 0 all these are quadratic equation 2.5x square minus 11 by 21x plus 14 or 42 is equal to 0 this is all these are all quadratic equations what are not quadratic equations which type of equations are not quadratic equations so not quadratic right so these are not quadratic equations quadratic equations what which all equations are not quadratic so if you see x minus y equals to 0 is not a quadratic equation y the degree is simply 1 then 2x cube minus 4x plus 5 equals to 0 this is also not a quadratic equation y because degree is 3 so x square plus 1 upon x square is equal to 0 this is also not a quadratic equation why because here if you see here this is first of all this is not a polynomial itself and secondly the power here is if you see this is nothing but x square plus x to the power minus 2 equals to 0 this doesn't fall under polynomial itself so hence it is not a quadratic equation similarly x square 4x square minus root 2 into root x plus 17 equals to 0 again not a quadratic equation y power of x here is half which is not allowed this is not a polynomial not a quadratic equation okay there could be a cases few cases where we can convert a non quadratic into a quadratic form for example this one could be reduced to a quadratic by some substitution which we'll see later but in this form it is not quadratic okay now quadratic equation could be in multiple variables also so I can say quadratic equation in two variables also is possible how so if you see quadratic equation two variables will be of the form of x square plus y square minus 2xy plus 7x minus 2y plus 5 equals so this is a quadratic equation in two variables similarly multiple variable quadratic equation is also possible but we are going to study quadratic equation of the form of ax square plus bx plus c equals 0 a not equal to 0 and a b c all are real numbers okay so in the subsequent session we'll see how to solve quadratic equation and other attached associated properties thank you