 Hi and welcome to the session. I am Neha and I am going to help you with the following question. The question says, find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients. And the quadratic polynomial is 3x square minus x minus 4. Let us proceed with its solution. We are given the polynomial 3x square minus x minus 4. Here first of all we will factorize the given polynomial by splitting its middle term. So we will split the middle term that is minus x in such a way that the sum of the two terms is minus x and their product is equal to the product of 3x square minus 4 that is minus 12x square. So this can be written as 3x square minus 4x plus 3x minus 4. So we have split minus x in minus 4x plus 3x that is minus 4x plus 3x is equal to minus x and their product is minus 12x square. Now let us take the common factor outside. In 3x square minus 4x we have a common factor x. So inside the bracket we are left with 3x minus 4. Now here in the last two terms we have a common factor that is 1. So we will take plus 1 as common and we are left with 3x minus 4. Now again in these two terms we have a common factor 3x minus 4. So let us take it outside and inside the bracket we are left with x plus 1. So this gives us 3x minus 4 into x plus 1. So these are the two factors of the given polynomial. Now if we consider the given polynomial as p of x then that means we got p of x as 3x minus 4 into x plus 1. Now we need to find the zeros of the polynomial p of x. So for that p of x will be equal to 0 when 3x minus 4 into x plus 1 will be equal to 0 or 3x minus 4 is equal to 0 or x plus 1 is equal to 0 that is x is equal to 4 upon 3 or x is equal to minus 1. Therefore zeros of p of x which is equal to 3x is square minus x minus 4 are 4 upon 3 and minus 1. Now we need to verify the relationship between the zeros and the coefficients. Here the coefficient of the x is square is 3, coefficient of x is minus 1 and the constant term is minus 4. So sum of zeros is equal to 4 upon 3 plus minus 1 that is equal to 4 upon 3 minus 1 upon 1 which will be 4 minus 3 upon 3 that is 1 upon 3. Now 1 upon 3 can be written as minus of minus 1 upon 3 and here minus 1 is the coefficient of x and 3 is the coefficient of x is square. So that means we can write it as minus coefficient of x upon coefficient of square. So we can say that sum of the zeros is equal to minus coefficient of x upon coefficient of x is square. Now let's see the product of zeros. This will be equal to 4 upon 3 into minus 1 that is minus 4 upon 3. Now here is the quadratic polynomial. Here minus 4 is the constant term. So we can write it as constant term upon 3 that is the coefficient of x is square. So this will be coefficient of x is square. Thus product of zeros is equal to constant term upon coefficient of x is square. Therefore our answer to this question is minus 1 comma 4 upon 3 which are the two zeros of the given quadratic polynomial. So with this we finish this session. Hope you must have understood the question. Goodbye, take care and have a nice day.