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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2007

  • question_answer
    If \[\alpha \] and \[\beta \] are the roots of the equation\[a{{x}^{2}}+\] \[bx+c=0,\text{ }\alpha \beta =3\] and a, b, c are in AP, then \[\alpha +\beta \]is equal to

    A)  \[-4\]

    B)                                         1

    C)  4                                            

    D)  \[-\,2\]

    E)  2

    Correct Answer: D

    Solution :

    Since,\[\alpha \]and\[\beta \]are the roots of the equation \[a{{x}^{2}}+bx+c=0\] \[\therefore \] \[\alpha +\beta =-\frac{b}{a}\] and \[\alpha \beta =\frac{c}{a}\] But \[\alpha \beta =3\] \[\therefore \] \[3=\frac{c}{a}\Rightarrow c=3a\]                                      ...(i) Also a, b, c are in AP. \[\therefore \]  \[b=\frac{a+c}{2}\] \[\Rightarrow \]               \[b=\frac{a+3a}{2}=2a\] Hence, \[\alpha +\beta =-\frac{b}{a}=-\frac{2a}{a}=-2\]


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