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

Now, product of zeroes,

\[\alpha \times \frac{1}{\alpha }=\frac{Constant\text{ }term}{Coefficient\,of\,{{x}^{2}}}\]

\[\Rightarrow 1=\frac{8k}{2}\]

\[\Rightarrow k=\frac{2}{8}=\frac{1}{4}\]