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Question
If α, β are the zeros of the polynomial f(x) = x2 + x + 1, then \[\frac{1}{\alpha} + \frac{1}{\beta} =\]
Options
1
-1
0
None of these
Solution
Since `alpha` and ß are the zeros of the quadratic polynomial f(x) = x2 + x + 1,
`alpha + ß = - (text{coefficient of x})/(text{coefficient of } x^2)`
`= (-1)/1=1`
`alpha + ß = (\text{constat term})/(text{coefficient of} x^2)`
`= 1/1=1`
we have
`= 1/alpha+ 1/ ß`
` (ß +alpha)/(alpha ß)`
`=-1/1`
`=-1`
The value of `1/alpha + 1/ß ` is -1
Hence, the correct choice is (b).
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