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Manipal Engineering Manipal Engineering 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)  (1, 2)                    

    B)  (0, 1)

    C)  (2, 3)              

    D)         (3, 4)

    Correct Answer: B

    Solution :

    Let\[f(x)=a{{x}^{2}}+bx+c\] Again, let\[f(x)=\int{f(x)}\,\,dx\]                 \[=\frac{a}{3}{{x}^{3}}+\frac{b{{x}^{2}}}{2}+cx\] At           \[x=0\]                 \[f(0)=0\] Again,   at\[x=1\]                 \[f(1)=\frac{a}{3}+\frac{b}{2}+c\]                 \[=\frac{2a+3b+6c}{6}=0\] Hence, one root lies between (0, 1).


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