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Question
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`2s^2 - (1 + 2sqrt(2))s + sqrt(2)`
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Solution
Let p(s) = `2s^2 - (1 + 2sqrt(2))s + sqrt(2)`
= `2s^2 - s - 2sqrt(2)s + sqrt(2)`
= `2s - 1 (s - sqrt(2))`
So, the zeroes of p(s) are `1/2` and `sqrt(2)`
∴ Sum of zeroes = `1/2 + sqrt(2)`
= `(1 + 2sqrt(2))/2`
= `(-[-(1 + 2sqrt(2))])/2`
= `(-("coefficient of" s))/("coefficient of" s^2)`
And product of zeroes = `1/2 . sqrt(2)`
= `"constant term"/("coefficient of" s^2)`
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