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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:
`v^2 + 4sqrt(3)v - 15`
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Solution
Let p(v) = `v^2 + 4sqrt(3)v - 15`
= `v^2 + 5sqrt(3)v - sqrt(3)v - 15`
= `(v + 5sqrt(3)) (v - sqrt(3))`
So, the zeroes of p(v) are `5sqrt(3)` and `sqrt(3)`
∴ Sum of zeroes = `-5sqrt(3) + sqrt(3) = -4sqrt(3)`
= `(-("coefficient of" v))/("coefficient of" v^2)`
And product of zeroes = `(-5sqrt(3))(sqrt(3))`
= –5 × 3
= –15
= `"constant term"/("coefficient of" v^2)`
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