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9th Class Mathematics Polynomials Question Bank Polynomials

  • question_answer
    If a, b, c are all non-zeroes and \[a+b+c=0,\]then \[\frac{{{a}^{2}}}{bc}+\frac{{{b}^{2}}}{ca}+\frac{{{c}^{2}}}{ab}=\_\_\_\_\_.\]

    A)  0                    

    B)         1                    

    C)  2                                

    D)  3

    Correct Answer: D

    Solution :

    We have, \[a+b+c=0\] \[\therefore \]\[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}=3abc\]                                ?(i) Now, \[\frac{{{a}^{2}}}{bc}+\frac{{{b}^{2}}}{ca}+\frac{{{c}^{2}}}{ab}=\frac{{{a}^{3}}+{{b}^{3}}+{{c}^{3}}}{abc}\] \[\frac{1}{abc}=(3abc)=3\]                    [Using (i)


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