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Question
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
t2 – 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)`
`-sqrt15xxsqrt15=(-15)/1`
`-15=-15`
Thus, the relationship between zeroes and the coefficients in the polynomial t2 - 15 is verified.
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