10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

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

A) \[q-1\]

B) \[1-q\]

C) \[q\]

D) \[1+q\]

Correct Answer: B

Solution :

[b] The given polynomial is

\[f(x)={{x}^{2}}-p(x+1)-q={{x}^{2}}-px-p-q\] Now,\[\alpha +\beta =-\frac{(-p)}{1}=p\]and \[\alpha \beta =\frac{-p-q}{1}=-p-q\]

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,(\alpha +1)\,(\beta +1)=\alpha \beta +\alpha +\beta +1\]

\[=-p-q+p+1=1-q\]