2. Solved Papers
  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2002

  • question_answer
    If\[{{x}^{2}}+px+q=0\]is the quadratic equation whose roots are\[a-2\]and\[b-2\]where a and b are the roots of\[{{x}^{2}}-3x+1=0,\]then:

    A)  \[p=1,q=5\]     

    B)                         \[p=5,q=1\]

    C)                         \[p=1,q=1\]                      

    D)                         \[p=1,q=-1\]

    E)                         none of these

    Correct Answer: D

    Solution :

    \[\because \]a and b are the roots of equation \[{{x}^{2}}-3x+1=0\] \[\therefore \]\[a+b=3\]and\[ab=1\]. Now, the given roots are\[a-2\]and\[b-2\] \[\therefore \]Sum of roots \[=a-2+b-2\] \[=3-4=-1\] and product of roots\[=(a-2)(b-2)\] \[=ab-2(a+b)+4\]                 \[=1-6+4=-4\] \[\therefore \]Required equation is\[{{x}^{2}}+x-1=0\] which is equivalent to\[{{x}^{2}}+px+q=0\] \[\therefore \] \[p=1\] and\[q=-1\]


You need to login to perform this action.
You will be redirected in 3 sec spinner