 Hi, so we are going to deal with this question in this session. It says form the equation whose roots are 2 plus root 3 and 2 minus root 3. So two roots are given and we have to form an equation clearly. This is if an equation has two roots then it will be a quadratic equation. We dealt with it in the previous sessions and how do we form an equation if we know the roots. So the method is this. So we know that an equation whose roots alpha beta are known is nothing but x square minus sum of minus sum of roots times x plus product of product of roots equals 0. This is the given equation, right? So hence it is x square minus sum of roots. So what are the roots? 2 plus root 3 plus 2 minus root 3. This is the sum of the roots times x plus product of the roots, which is nothing but 2 plus root 3 times 2 minus root 3 and this must be equal to 0. This is a given equation. So hence let's simplify. This is nothing but x square and this root 3 root 3 will get cancelled. So hence it is minus 4x and plus 2 square minus root 3 square because this is of the form a plus b, a minus b equals, right? So this equals 0. So hence the final answer or the equation is x square minus 4x plus 4 minus 3 is equal to 0 or x square minus 4x plus 1 equals 0. This is the requisite. This is the equation which is required here and hence if you solve any method which we have learned so far, you will get that this is the equation whose roots are 2 plus root 3 and 2 minus root 3. The same question could have been solved by the fact that if or we can base the argument on factor theorem and we can say that if alpha and beta are roots or from the brief fact that or that if alpha and beta are rather than roots if I say zeros, zeros of a polynomial, polynomial then x minus alpha and x minus beta are factors, factors of the polynomial, right? So using this also this can be solved. So hence we can say the equation could be x minus alpha times x minus beta equals 0. So this happens to be the polynomial which I am writing as x minus alpha and x minus beta this equals 0. When you get to 0, you will get the quadratic equation. So hence what is it? x minus first root is 2 plus root 3 and this into x plus sorry x minus x minus 2 minus root 3 times, right? So this is equal to 0. When you simplify this you will again get x square minus 4x plus 1 equals to 0. These are the two methods of finding an equation, finding an equation whose roots are given.