A) \[3{{x}^{2}}+3\]
B) \[{{x}^{2}}-3x\]
C) \[{{x}^{2}}+3x\]
D) \[3{{x}^{2}}-3\]
Correct Answer: C
Solution :
Let \[\alpha \] and \[\beta \] be the zeroes of the required polynomial. |
Given, \[\alpha =-3\]and \[\alpha \cdot \beta =0\] |
\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,-3\cdot \beta =0\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\beta =0\] |
Now, required polynomial |
\[={{x}^{2}}-(\alpha +\beta )x+\alpha \beta \] |
\[={{x}^{2}}-(-3+0)x+(-3)\,(0)={{x}^{2}}+3x\] |
So, option [c] is correct. |
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