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`

Answer 1

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)`