Question

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`2s^2 - (1 + 2sqrt(2))s + sqrt(2)`

Answer 1

Let p(s) = `2s^2 - (1 + 2sqrt(2))s + sqrt(2)`

= `2s^2 - s - 2sqrt(2)s + sqrt(2)`

= `2s - 1 (s - sqrt(2))`

So, the zeroes of p(s) are `1/2` and `sqrt(2)`

∴ Sum of zeroes = `1/2 + sqrt(2)`

= `(1 + 2sqrt(2))/2`

= `(-[-(1 + 2sqrt(2))])/2`

= `(-("coefficient of"  s))/("coefficient of"  s^2)`

And product of zeroes = `1/2 . sqrt(2)`

= `"constant term"/("coefficient of"  s^2)`