Question

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

`p(x) = x^2 + 2sqrt2x + 6`

Answer 1

`p(x)=x^2+2sqrt2x-6`

= `x^2+3sqrt2x+sqrt2xx3sqrt2`

= `x(x+3sqrt2)-sqrt2(2+3sqrt2)`

= `(x-sqrt2)(x+3sqrt2)`

Zeroes of the polynomial are `3sqrt2` and `-3sqrt2`

Sum of the zeroes `=(-3sqrt2)/1`

`sqrt2-3sqrt2`

= `-2sqrt2`

`-2sqrt2=-2sqrt2`

Product of zeroes `=sqrt2xx(-3sqrt2)=-6/1`

`-6=-6`

Hence the relationship verified