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If one roots of the equation x^(2)-sqrt(...

If one roots of the equation `x^(2)-sqrt(5)x-19=0` is `(9+sqrt(5))/2` then find the other root.

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All coefficients of the given equation are not rationa, then other root `!=(9-sqrt(5))/2`
Let other root be `alpha` sum of roots `=sqrt(5)`
`=(9+sqrt(5))/2+alpha=sqrt(5)impliesalpha=(-9+sqrt(5))/2`
Hence other root is `(-9+sqrt(5))/2`
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