10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

If \[\alpha \] and \[\beta \] are zeroes and the quadratic polynomial \[f(x)={{x}^{2}}-x-4,\] then the value of \[\frac{1}{\alpha }+\frac{1}{\beta }-\alpha \beta \] is:

A) \[\frac{15}{4}\]

B) \[\frac{-15}{4}\]

C) \[4\]

D) \[15\]

Correct Answer: A

Solution :

[a] Given that, \[f(x)={{x}^{2}}-x-4\]

\[\alpha +\beta =1\]

and \[\alpha \beta =-4\]

We have,

\[\frac{1}{\alpha }+\frac{1}{\beta }-\alpha \beta =\frac{\alpha +\beta }{\alpha \beta }-\alpha \beta =-\frac{1}{4}+4=\frac{15}{4}\]