KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    If the quadratic equation \[f\,(x)=p{{x}^{2}}-qx+r=0\] has two distinct roots in (0, 2) where p, q, \[r\in N\] and \[f\,(1)=-1\] then the minimum value of p is

    A) 1

    B) 2

    C) 4

    D) none of these

    Correct Answer: B

    Solution :

    \[f\,(1)=p-q+r=-1\] ?(i)
    \[f\,(0)=r>0\] ?(ii)
    \[f\,(2)=4p-2q+r>0\] ?(iii)
    (ii) + (iii) \[\Rightarrow \]\[4p-2q+2r>0\]
                            \[p+(p-q+r)>0\]      [using (i)]
                            \[p-1>0\]           \[\Rightarrow \]\[p>1\]
    \[\therefore \]      \[p=2\]              \[(\because p\in N)\]

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