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JEE Main & Advanced Sample Paper JEE Main Sample Paper-18

  • question_answer
    Number of values of \[x\] satisfying the pair of quadratic equations \[{{x}^{2}}-px+20=0\] and \[{{x}^{2}}-20x+p=0\]for some\[p\in R,\]is

    A)  0                                            

    B)  1

    C)  2                                            

    D)  3

    Correct Answer: D

    Solution :

     Given equations are \[{{x}^{2}}-px+20=0\] \[{{x}^{2}}-20x+p=0\] If \[p=20\] then the quadratic equations are identical. Hence\[x=10+4\sqrt{5}\]or \[x=10-4\sqrt{5}\]. If \[p\ne 20\]then subtracting equations, we get \[(20-p)x+(20-p)=0\] \[\Rightarrow \] \[x=-1\]and\[p=-\,21\] Hence there are 3 values of\[x\].


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