 Hello and welcome to the session. In this session we discussed the following question which says find the quadratic polynomial whose 0's are 1 upon 2 and 1 upon 3. We know that a quadratic polynomial whose 0's are alpha and beta is given by px is equal to x square minus alpha plus beta into x plus alpha beta. This is the key idea to be used in this question. Let's move on to the solution now. Now we are given that the 0's of the quadratic polynomial 1 upon 2 and 1 upon 3, we take let alpha be equal to 1 upon 2 and beta be equal to 1 upon 3. That is we have alpha and beta are the 0's of the quadratic polynomial. Then alpha plus beta is equal to 1 upon 2 plus 1 upon 3 and this is equal to, taking LCM we get 6 in the denominator and in the numerator we have 3 plus 2. So we get this is equal to 5 upon 6 that is alpha plus beta is equal to 5 upon 6. Now the product of the 0's that is alpha beta is equal to 1 upon 2 into 1 upon 3. Therefore we get alpha beta is equal to 1 upon 6. Now the required polynomial say px is given by x square minus sum of the 0's of the polynomial into x plus the product of the 0's. So px would be equal to x square minus 5 upon 6 into x plus the product that is 1 upon 6. So this is equal to x square minus 5 upon 6 into x plus 1 upon 6. This is our required polynomial px so this means we get px is equal to 6x square minus 5x plus 1. So this is the required polynomial that is we say that px equal to 6x square minus 5x plus 1 is the quadratic polynomial with 0's 1 upon 2 and 1 upon 3. So this completes the session hope you have understood the solution for this question.