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J & K CET Engineering J and K - CET Engineering Solved Paper-2013

  • question_answer
    In a three dimensional space the equation \[{{x}^{2}}-5x+6=0\]represents

    A)  points             

    B)  planes

    C)  curves             

    D)  None of these

    Correct Answer: B

    Solution :

    Given equation is \[{{x}^{2}}-5x+6=0\] ?.(i) we know that the standard equation of plane in three dimensional space is \[ax+by+cz+d=0\] Now, from Eq. (i) \[{{x}^{2}}-3x-2x+6=0\] \[\Rightarrow \] \[x(x-3)-2(x-3)=0\] \[\Rightarrow \] \[(x-3)(x-2)=0\] \[\therefore \] \[x-3=0\] and \[x-2=0\] \[\Rightarrow \] \[1.x+0.y+0.z-3=0\] and \[1.x+0.y+0.z-2=0\] So, both represents equations of plane.


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