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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:
`y^2 + 3/2 sqrt(5)y - 5`
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Solution
Let p(y) = `y^2 + 3/2 sqrt(5)y - 5`
= `2y^2 + 3sqrt(5)y - 10`
= `2y^2 + 4sqrt(5)y - sqrt(5)y - 10`
= `(y + 2sqrt(5))(2y - sqrt(5))`
So, the zeroes of p(y) are `-2sqrt(5)` and `sqrt(5)/2`
∴ Sum of zeroes = `-2sqrt(5) + sqrt(5)/2`
= `(-3sqrt(5))/2`
= `(-("coefficient of" y))/("coefficient of" y^2)`
And product of zeroes = `-2sqrt(5) xx sqrt(5)/2` = –5
= `"constant term"/("coefficient of" y^2)`
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