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

If a and p be the zeroes of the polynomial \[{{x}^{2}}-1,\]then the value of \[\frac{1}{\alpha }+\frac{1}{\beta }\]is:

A) \[0\]

B) \[\frac{1}{2}\]

C) \[1\]

D) \[-1\]

Correct Answer: A

Solution :

Let \[p(x)={{x}^{2}}-1\]

Now, sum of zeroes \[=-\frac{\text{Coefficient of x}}{\text{Coefficient of }{{\text{x}}^{2}}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\alpha +\beta =-\frac{0}{1}=0\]

and product of zeroes \[=\frac{\text{Constant}\,\,\text{term}}{\text{Coefficient of }{{\text{x}}^{2}}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\alpha \cdot \beta =\frac{-1}{1}=-1\]

\[\therefore \,\,\,\,\,\,\,\,\,\frac{1}{\alpha }+\frac{1}{\beta }=\frac{\alpha +\beta }{\alpha \beta }=\frac{0}{-1}=0\]

So, option [a] is correct.