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Question
If one root of the polynomial f(x) = 5x2 + 13x + k is reciprocal of the other, then the value of k is
Options
0
5
- \[\frac{1}{6}\]
6
Solution
If one zero of the polynomial f(x) = 5x2 + 13x + k is reciprocal of the other. So `beta = 1/alpha ⇒`
Now we have
`alphaxxbeta= (\text{Constant term})/(\text{Coefficient of}x^2)`
`= k /5`
Since`alphabeta =1`
Therefore we have
`alpha beta = k/5`
`1= k/5`
`⇒ k = 5`
Hence, the correct choice is `(b)`.
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