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Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients:

t^{2} – 15

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#### Solution

h(t) `=t^2-15`

`=(t)^2-(sqrt15)^2`

`=(t+sqrt15)(t-sqrt15)`

For p(t) = 0, we have

Either `(t + sqrt15) = 0`

`t = sqrt15`

or `t - sqrt15 = 0`

`t = sqrt15`

Sum of the zeroes =`-("coefficient of " t)/("coefficient of " t^2)`

`-sqrt15+sqrt15=(-0)/1`

0 = 0

Also product of the zeroes =` "constant term"/("coefficient of " t^2)`

`=(-15)/1`

`-sqrt15xxsqrt15=(-15)/1`

`-15=-15`

Thus, the relationship between zeroes and the coefficients in the polynomial t^{2} - 15 is verified.

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