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11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-7

  • question_answer
    If the roots of \[{{\mathbf{x}}^{\mathbf{2}}}-\mathbf{bx}+\mathbf{c}=\mathbf{0}\]are two consecutive integers, then \[{{b}^{2}}-4ac\]is

    A)  1                   

    B)  2              

    C)  0                                

    D)  3

    Correct Answer: A

    Solution :

    [a] \[\because \]Let \[\alpha ,\alpha +1\]be the roots of equation \[{{x}^{2}}-bx+c=0\] \[\therefore \alpha +\alpha +1=b\] \[\alpha \left( \alpha +1 \right)=c\] \[\because {{b}^{2}}-4ac={{(2\alpha +1)}^{2}}-4.1.\alpha (\alpha +1)\] \[=4{{\alpha }^{2}}+4\alpha +1-4{{\alpha }^{2}}-4\alpha \] = 1 [Here\[a=1\]] Hence, option [a] is correct.


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