10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

If \[\alpha ,\beta \] are the zeroes of the polynomial \[p(x)={{x}^{2}}-2x-3,\]then \[\frac{1}{\alpha }+\frac{1}{\beta }\] is:

A) \[\frac{2}{3}\]

B) \[\frac{1}{3}\]

C) \[\frac{-1}{3}\]

D) \[-\frac{2}{3}\]

Correct Answer: D

Solution :

[d] Since \[\alpha ,\beta \] are zeroes of the polynomial

\[p(x)={{x}^{2}}-2x-3,\]

Then, sum of zeroes \[=\alpha +\beta =\frac{-(-2)}{1}=2\]

and product of zeroes \[=\alpha \beta =\frac{-3}{1}=-3\]

Now, \[\frac{1}{\alpha }+\frac{1}{\beta }=\frac{\alpha +\beta }{\alpha \beta }=-\frac{2}{3}\]