JEE Main & Advanced Mathematics Quadratic Equations Question Bank Critical Thinking

  • question_answer 21) If 8, 2 are the roots of \[{{x}^{2}}+ax+\beta =0\] and 3, 3 are the roots of \[{{x}^{2}}+\alpha \,x+b=0\], then the roots of \[{{x}^{2}}+ax+b=0\] are [EAMCET 1987]

    A) \[8,\,-1\]

    B) - 9, 2

    C) \[-8,-2\]

    D) 9, 1

    Correct Answer: D

    Solution :

    8, 2 are the roots of \[{{x}^{2}}+ax+\beta =0\] \ \[8+2=10=-a\],\[8.2=16=\beta \] i.e. \[a=-10,\beta =16\] 3, 3 are the roots of \[{{x}^{2}}+\alpha x+b=0\] \ \[3+3=6=-\alpha ,\,\,3.3=b\] i.e. \[\alpha =-6,b=9\] Now, \[{{x}^{2}}+ax+b=0\]becomes \[{{x}^{2}}-10x+9=0\] or\[(x-1)(x-9)=0\Rightarrow x=1,\,9\].

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