10th Class Mathematics Polynomials Question Bank Case Based (MCQs) - Polynomials

If \[\alpha \] and \[\frac{1}{\alpha }\]are the zeroes of the quadratic polynomial \[2{{x}^{2}}-x+8k,\] then k is:

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.