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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:
`7y^2 - 11/3 y - 2/3`
Solution
Let p(y) = `7y^2 - 11/3 y - 2/3`
= 21y2 – 11y – 2
= 21y2 – 14y + 3y – 2
= (3y – 2)(7y + 2)
So, the zeroes of p(y) are `2/3` and `-1/7`
∴ Sum of zeroes = `2/3 - 1/7`
= `11/21`
= `-((-11)/(3 xx 7))`
= `(-("coefficient of" y))/("coefficient of" y^2)`
And product of zeroes = `(2/3)(-1/7)`
= `(-2)/(3 xx 7)`
= `"constant term"/("coefficient of" y^2)`
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