JEE Main & Advanced Mathematics Quadratic Equations Question Bank Critical Thinking

  • question_answer 29) 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 [Kerala (Engg.) 2002]

    A) \[p=1,\,q=5\] 

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

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

    D) None of these

    Correct Answer: D

    Solution :

    \[a+b=3\], \[ab=1\] and\[-p=a-2+b-2\],\[q=(a-2)(b-2)\] Þ \[-p=a+b-4\], \[q=ab-2(a+b)+4\] \[\Rightarrow -p=3-4\] and\[q=1-2(3)+4\] Þ \[(p,\,q)=(1,\,-1)\].

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