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Railways Sample Paper RRB (Group D) Sample Test Paper-7

  • question_answer
    If the HCF of\[{{x}^{3}}+m{{x}^{2}}-\,x+2\,\,m\] and\[{{x}^{2}}+mx-\,2\] is a linear polynomial, then what is the value of m?

    A)  1                    

    B)  2

    C)  3                    

    D)  4

    Correct Answer: A

    Solution :

    Let \[{{f}_{1}}\,\,(x)={{x}^{3}}+m{{x}^{2}}-\,x+2\,\,m\] and \[{{f}_{2}}\,\,(x)={{x}^{2}}+mx-2\] Let \[m=1\] \[\therefore {{f}_{1}}\,\,(x)={{x}^{3}}+{{x}^{2}}-\,x+2\] and \[{{f}_{2}}\,\,(x)={{x}^{2}}+x-\,2=(x+2)\,\,(x-\,1)\] When \[x=1,\] \[f\,\,(1)=1+1-1+2\ne 0\] When \[x=-\,2\] \[f\,\,(-2)={{(-2)}^{3}}+{{(-\,2)}^{2}}-\,(-\,2)+2=0\] Required value of m is 1.


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