Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials (x) `7y^(2)-(11)/(3)y -(2)/(3)`

Find the zeroes of the following polynomials by factorisation method a

1.	Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials (x) `7y^(2)-(11)/(3)y -(2)/(3)`
Answer» Let `f(y) = 7y^(2)-(11)/(3)y -(2)/(3)` `= 21 y^(2) - 11y - 2` `= 21y^(2) - 14y +3y -2` [by splitting the middle term] `=7y (3y -2)+1(3y -2)` `=(3y-2) (7y+1)` So, the value of `7y^(2)-(11)/(3)y -(2)/(3)` is zero when `3y - 2 = 0` or `7y +1 = 0`. i.e., when `y = (2)/(3)` or `y =- (1)/(7)`. So, the zeroes of `7y^(2) -(11)/(3)y - (2)/(3)` are `(2)/(3)` and `-(1)/(7)` `:.` Sum of zeroes `= (2)/(3)-(1)/(7) =(14-3)/(21) =(11)/(21) = -((-11)/(3xx7))` `=(-1) (("Coefficient of y"))/(("Coefficient of" y^(2)))` and product of zeroes `= ((2)/(3)) (-(1)/(7)) =(-2)/(21) = (-2)/(3xx7)` `= (-1)^(2) (("Constant term")/("Coefficient of " y^(2)))` Hence, verified the relations between the zeroes and the coefficients of the polynomial.