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SSC Sample Paper Mock Test-8 SSC CGL Tear-II Paper-1

  • question_answer
    A and B solved a quadratic equation. In solving it, A made a mistake in the constant term and obtained the roots as 6 and 2, while B made a mistake in the coefficient of x only and obtained the roots \[-\,\,7\]and \[-1.\]Find the correct roots of the equation.

    A) 7, 1      

    B)  2, 5

    C) \[-\,\,6,3\]

    D)  \[-\,\,7,1\]

    Correct Answer: A

    Solution :

    As obtained by A, we have \[\alpha +\beta =8\] and \[\alpha \beta =12\]
    \[\therefore \]The equation is \[{{x}^{2}}-8x+12=0\]
    As obtained by JS, we have \[\alpha +\beta =-\,\,8\] and \[\alpha \beta =7\]
    \[\therefore \]The equation is \[{{x}^{2}}+8x+7=0\]
    Hence, the correct equation is \[{{x}^{2}}-8x+7=0\]
    Now, \[{{x}^{2}}-8x+7=0\] \[\Rightarrow \]\[{{x}^{2}}-7x-x+7=0\]
    \[\Rightarrow \]\[x\,\,(x-7)-(x-7)=0\] \[\Rightarrow \]\[(x-7)(x-1)=0\]
    \[\Rightarrow \]\[x=7\] or \[x=1\]


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