A) \[4\]
B) \[\frac{1}{4}\]
C) \[\frac{-1}{4}\]
D) \[2\]
Correct Answer: B
Solution :
Given that, \[\alpha \] and \[\frac{1}{\alpha }\] are the zeroes of the quadratic polynomial \[2{{x}^{2}}-x+8k.\] |
\[\therefore \] Product of zeroes \[\frac{\text{Constant term}}{\text{Coefficient of }{{\text{x}}^{2}}}\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\alpha +\frac{1}{\alpha }=\frac{Bk}{2}\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,8k=2\Rightarrow k=\frac{1}{4}\] |
So, option [b] is correct. |
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