Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials
(v) `2x^(2)+(7)/(2)x+(3)/(4)`

Explanation

Let `f(x) = 2x^(2)+(7)/(2)x+(3)/(4) = 8x^(2)+14x +3`
`= 8x^(2)+12x +2x +3` [by splitting the middle term]
`=4x (2x+3) +1(2x+3)`
`= (2x+3) (4x+1)`
So, the value of `8x^(2)+14x =3` is zero when `2x +3 = 0` or `4x +1 = 0`.
i.e., when `x =- (3)/(2)` or `x =- (1)/(4)`
So, the zeroes of `8x^(2) +14x +3` are `-(3)/(2)` and `-(1)/(4)`
`:.` Sum of zeroes `=-(3)/(2) -(1)/(4)=-(7)/(4) = (-7)/(2xx2)`
`=-(("Coefficient of x"))/(("Coefficient of" x^(2)))`
And roduct of zeroes `= (-(3)/(2))(-(1)/(4)) = (3)/(8) = (3)/(2xx4)`
`= ("Constant term")/("Coefficient of" x^(2)))`
Hence, verified the relations between the zeroes and the coefficient of the polynomial.