Let `f(y) =y^(2)+(3)/(2) sqrt(5)y - 5`
`= 2y^(2) +3sqrt(5)y - 19`
`= 2y^(2) +4sqrt(5) y - sqrt(5)y - 10` [by splitting the middle term]
`=2y (y+2sqrt(5)) - sqrt(%) (y+2sqrt(5))`
`= (y+2sqrt(5)) (2y-sqrt(5))`
So, the value of `y^(2)+(3)/(2) sqrt(5)y - 5` is zero when `(y+2sqrt(5)) =0` or `(2y - sqrt(5)) = 0`
i.e., when `y =- 2sqrt(5)` or `y = (sqrt(5))/(2)`.
So, the zeroes of `2y^(2) +3sqrt(5)y - 10` are `-2sqrt(5)` and `(sqrt(5))/(2)`
`:.` Sum of zeroes `=- 2sqrt(5)+(sqrt(5))/(2)=(-3sqrt(6))/(2) =- (("Coefficient of y"))/(("Coefficient of" y^(2)))`
And product of zeroes `=0 2sqrt(5) xx (sqrt(5))/(2)=- 5 = ("Constant term")/("Coefficient of" y^(2))`
Hence, verified the relations between the zeroes and the coefficients of the polynomial.