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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 9

  • question_answer
    Number of common roots in the equations  \[{{x}^{4}}+2{{x}^{3}}+5{{x}^{2}}-6x-2=0\] and \[{{x}^{3}}+2{{x}^{2}}+4x-7=0\] is

    A) \[0\]                     

    B) \[1\]      

    C) \[2\]                    

    D) \[3\]

    Correct Answer: B

    Solution :

    [b] Let \[f(x)={{x}^{4}}+2{{x}^{3}}+5{{x}^{2}}-6x-2\] and \[g(x)={{x}^{3}}+2{{x}^{2}}+4x-7\] All common roots of \[f(x)=0\] and \[g(x)=0\] are roots of equation \[f(x)-xg(x)=0\]. \[\Rightarrow \,\,\,\,{{x}^{2}}+x-2=0\] Common roots may be \[x=1\] or \[x=-2\]. Bu t \[x=-2\] does not satisfy \[g(x)=0\]. Hence, the only common root is\[x=1\].         


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