 Hello and welcome to the session. In this session we will discuss a question which says that is it possible to have more than two roots of a quadratic equation? Now let us start with the solution. Now here let us take a quadratic equation A x square plus B x plus C is equal to 0 where A is not equal to 0. Now let P, Q and T are three different roots. Now when P is the root then according to the definition of the root it will satisfy this equation. So it will be A q square plus B p plus C is equal to 0. Let us name this equation as 1. When Q and T then two also will satisfy this equation. When Q is the root the equation will be A q square plus B q plus C is equal to 0 and when T is the root this equation will be A t square plus B t plus C is equal to 0. Let us name this equation as 2 and this equation as 3. Now selecting we get minus T square the whole plus T the whole plus C minus C is equal to 0. Now this implies the whole into Q plus T the whole. This is a formula of A square minus B square which is equal to A minus P into A plus B plus B into Q minus T the whole and here C and C will be cancelled so this will be equal to 0. Now this implies common and we do not like it is T the whole plus B is equal to 0. Since this is not equal to T our two different roots when we get T the whole plus B is equal to 0. Now let us take this as equation number 4 and this as equation number 5. Now subtracting we will write it as minus Q plus B minus B is equal to 0. This implies we write it as Q will be cancelled with Q so it will be T minus P and here B will be cancelled with B so it will be equal to 0. Now this implies P is equal to 0. Which implies now this condition qualifies the equation as a quadratic equation. A quadratic equation is the solution of the given question and that is all for this session. Hope you have enjoyed the session.