 Hello and welcome to the session. Let us discuss the following problem today. Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients. We have the polynomial f of x is equal to 6x square minus 3 minus 7x. Now let us understand the key idea for the problem. A real number alpha is a zero of a polynomial f of x is f of alpha is equal to 0. If alpha and beta are the coefficients of a quadratic polynomial f of x is equal to ax square plus vx plus c, then alpha plus beta is equal to minus v by a which is equal to minus coefficient of x by coefficient of x square and alpha beta is equal to c by a which is equal to constant term by coefficient of x square. Now let us write the solution for the problem. We have f of x is equal to 6x square minus 3 minus 7x which can be written as 6x square minus 7x minus 3. Now splitting the middle term we get 6x square minus 9x plus 2x minus 3. Now taking the common factor from the first two we get 3x common so we are left with 2x minus 3 and from here we take plus 1 common so we are left with 2x minus 3. Therefore we get 3x plus 1 and 2x minus 3 as our factors. We have, now we have f of x is equal to 3x plus 1 into 2x minus 3 and zeros of f of x are given by f of x is equal to 0 which implies 3x plus 1 into 2x minus 3 is equal to 0 which implies 3x plus 1 is equal to 0 or 2x minus 3 is equal to 0 which implies x is equal to minus 1 by 3 or x is equal to 3 by 2. Zeros of f of x are f is equal to minus 1 by 3 and zeta is equal to 3 by 2. Now the verification part. Key idea we have sum of zeros that is alpha plus beta is equal to minus 1 by 3 plus 3 by 2 which is equal to 7 by 6 that is minus coefficient of x divided by coefficient of x square which is equal to minus of minus 7 by 6 which is equal to 7 by 6. Similarly product of zeros that is alpha beta is equal to minus 1 by 3 into 3 by 2 which is equal to minus 1 by 2 that is constant term divided by coefficient of x square which is equal to minus 3 by 6 which is equal to minus 1 by 2. Hence verified. I hope you understood this problem. Bye and have a nice day.