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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`
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Solution
`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
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