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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        If\[2a+3b+6c=0,\] then at least one root of the equation\[a{{x}^{2}}+bx+c=0\]lies in the interval

    A)  (2, 3)                                    

    B)  (1, 2)

    C)  (0, 1)                                    

    D)  (1, 3)

    Correct Answer: C

    Solution :

                    Let\[f(x)=a{{x}^{2}}+bx+c,\] then      \[f(x)=\frac{a{{x}^{3}}}{3}+\frac{b{{x}^{2}}}{2}+cx+k\]                                 \[=\frac{2a{{x}^{3}}+3b{{x}^{2}}+6cx+6k}{6}\] \[\Rightarrow \]               \[f(1)=\frac{2a+3b+6c+6k}{6}=\frac{6k}{6}=k\] Also,          \[f(0)=\frac{6k}{6}=k\] \[\therefore \]  \[f(0)=f(1)=k\] \[\Rightarrow \]               \[f(x)=0\]


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