Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials
(iii) `5t^(2)+12t +7`.

Explanation

Let `f(t) = 5t^(2) +12t +7`
`= 5t^(2)+7t +5t +7` [by splitting the middle term]
`= t (5t +7) +1(5t +7)`
`= (5t+7) (t+1)`
So, the value of `5t^(2)+12t +7` is zero when `5t +7` or `t +1 = 0`
i.e., when `t = (-7)/(5)` or `t =- 1`.
So, the zeroes of `5t^(2) +12t +7` are `-7//5` and -1.
`:.` Sum of zeroes `=- (7)/(5) - 1 = (-12)/(5)`
`=(-1) (("Coefficient of t")/("Coefficient of" t^(2)))`
and product of zeroes `= (-(7)/(5)) (-1) = (7)/(5)`
`= (-1)^(2) (("Constant term")/("Coefficient of" t^(2)))`
Hence, verified the relations between the zeroes and the coefficients of the polynomial.