11th Class Mathematics Other Series Question Bank Critical Thinking

  • question_answer If the A.M. and G.M. of roots of a quadratic equations are 8 and 5 respectively, then the quadratic equation will be [Pb. CET 1990]

    A) \[{{x}^{2}}-16x-25=0\]

    B) \[{{x}^{2}}-8x+5=0\]

    C) \[{{x}^{2}}-16x+25=0\]

    D) \[{{x}^{2}}+16x-25=0\]

    Correct Answer: C

    Solution :

    Given that \[A.M.=8\] and \[G.M.=5\], if \[\alpha ,\ \beta \] are roots of quadratic equation, then quadratic equation is \[{{x}^{2}}-x(\alpha +\beta )+\alpha \beta =0\]             ......(i) \[A.M.=\frac{\alpha +\beta }{2}=8\]\[\Rightarrow \]\[\alpha +\beta =16\]      ......(ii) and \[G.M.=\sqrt{\alpha \beta }=5\]\[\Rightarrow \]\[\alpha \beta =25\]      ......(iii) So the required quadratic equation will be \[{{x}^{2}}-16x+25=0\].

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