10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

The zeroes of the polynomial \[{{x}^{2}}-3x-m(m+3)\] are: (CBSE 2020)

A) \[m,\,\,m+3\]

B) \[-m,\,\,m+3\]

C) \[m,-(\,\,m+3)\]

D) \[-m,-(\,\,m+3)\]

Correct Answer: B

Solution :

[b] Let \[f(x)={{x}^{2}}-3x-m(m+3)\]

\[={{x}^{2}}-\{(m+3)-m\}x-m(m+3)\]

\[={{x}^{2}}-(m+3)x+mx-m(m+3)\]

\[=\{x-(m+3)\}+m\{x-(m+3)\}\]

\[=\{x-(m+3)\}(x+m)\]

For zeroes of \[f(x),\]

\[\{x-(m+3)\}\,(x+m)=0\]

\[x-(m+3)=0\] or \[x+m=0\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=-m,(m+3)\]