 Hello and welcome to the session. Let us discuss the following problem. Find the zeroes of the following quadratic polynomial and verify the relationship between the zero and the coefficient fx is equal to x square minus 2x minus 8. Let us write the key idea. A real number alpha is the zero of a polynomial f of x if f of alpha is equal to 0 and if alpha and beta are the coefficients of a quadratic polynomial f of x is equal to A x square plus B x plus c alpha plus beta is equal to minus B by A that is minus coefficient of x divided by coefficient of x square and alpha beta is equal to c by A which is equal to constant term divided by coefficient of x square. Now let us write the solution for the problem. Now the solution. We have f of x is equal to x square minus 2x minus 8. Now we will split the middle term x square minus 4x plus 2x minus 8. Now grouping and taking common factors from these two terms we take x common so we are left with x minus 4 and from these two terms we take plus 2 common and we are left with x minus 4. Now we get x plus 2 into x minus 4 as our factors which is equal to f of x therefore zeros of f of x are given by equating f of x is equal to 0 which implies x plus 2 into x minus 4 is equal to 0 which implies x plus 2 is equal to 0 or x minus 4 is equal to 0 which implies x is equal to minus 2 or x is equal to 4 thus the zeros of f of x is equal to f minus 2x minus 8 are alpha is equal to minus 2 and beta is equal to 4. Now second part of the question to verify the relationship between the zeros and the coefficient here sum of the zeros plus beta is equal to minus 2 plus 4 which is equal to 2 that is minus coefficient of x divided by coefficient of x square which is equal to minus 2 by 1. Similarly product of zeros is equal to alpha beta which is equal to minus 2 into 4 which is equal to minus 8 by 1 which is equal to constant term by coefficient of x that is minus 8 by 1 hence verified. I hope you enjoyed this session. Bye and have a nice day.