question_answer

If a, b, c are positive integers, then the determinant  is divisible by            

A) \[{{x}^{3}}\]              

B) \[{{x}^{2}}\]

C) \[({{a}^{2}}+{{b}^{2}}+{{c}^{2}})\]        

D)  None of these

Correct Answer: B

Solution :

[b]: Clearly, (Applying\[{{R}_{1}}\to {{R}_{1}}+{{R}_{2}}+{{R}_{3}}\]) \[={{x}^{2}}({{a}^{2}}+{{b}^{2}}+{{c}^{2}}+x)\] Hence \[\Delta \]is divisible by \[{{x}^{2}}\] as well as by x.