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`

Answer 1

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)`