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`

Answer 1

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)`