 Hi and welcome to the session. Today I will help you with the following question which says find the zeros of the quadratic polynomial 6x square minus 3 minus 7x and verify the relationship between the zeros and the coefficients of the polynomial. Before moving on to the solution, let's recall the relationship between the zeros and the coefficients of the polynomial. Suppose we have a polynomial ax square plus vx plus c, then sum of its zeros will be equal to minus of coefficient of x upon coefficient of x square. And product of its zeros will be equal to constant term upon coefficient of x square. This is the key idea for this question. Now let us proceed with its solution. We are given the quadratic polynomial 6x square minus 3 minus 7x which can also be written as 6x square minus 7x minus 3. Now let us factorize this quadratic polynomial by splitting its middle term. Its middle term is minus 7x, so we will split minus 7x as minus 9x plus 2x because minus 9x plus 2x is minus 7x and minus 9x into 2x is equal to minus 18x square which is equal to 6x square into minus 3. So this polynomial will become 6x square minus 9x plus 2x minus 3. Now from the first two terms let us take 3x common so we will get 3x into 2x minus 3. Now from the last two terms let us take plus 1 as common and we are left with 2x minus 3. So this will be equal to 2x minus 3 into 3x plus 1. Thus 2x minus 3 and 3x plus 1 are the factors of the given quadratic polynomial 6x square minus 3 minus 7x. Now to find out the zero of the given quadratic polynomial we will equate this quadratic polynomial to 0. So value of 6x square minus 3 minus 7x is 0 when either 2x minus 3 will be equal to 0 or 3x plus 1 will be equal to 0. That is when x will be equal to 3 upon 2 or x will be equal to minus 1 upon 3. Therefore zeros of 6x square minus 3 minus 7x are 3 upon 2 and minus 1 upon 3. Now we need to verify the relationship between the zeros and the coefficients of the polynomial. So first of all let us find the sum of zeros which will be equal to 3 upon 2 plus minus 1 upon 3 that is 9 minus 2 upon 6 which is equal to 7 upon 6. Now in the given quadratic polynomial minus 7 is the coefficient of x and 6 is the coefficient of x square. So 7 upon 6 is equal to minus of coefficient of x upon coefficient of x square. Now let us find the product of zeros which will be equal to 3 upon 2 into minus 1 upon 3 which is equal to minus 3 upon 6. And in the given quadratic polynomial minus 3 is the constant term and 6 is the coefficient of x square. So this is equal to constant term upon coefficient of x square. Thus we have verified the relationship between the zeros and the coefficients of the polynomial. With this we finish this session. Hope you must have understood the question. Goodbye, take care and keep smiling.