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Let P(x) and Q(x) be two quadratic polyn...

Let `P(x)` and `Q(x)` be two quadratic polynomials such that minimum value of `P(x)` is equal to twice of maximum value of `Q(x)` and `Q(x)>0AA x in(1, 3)` and `Q (x)<0AA x in(-oo, 1)uu(3, oo)`. If sum of the roots of the equation `P(x)=0` is 8 and `P(3)-P(4)=1` and distance between the vertex of `y=P(x)` and vertex of `y=Q(x)` is `2sqrt(2)` The polynomial `P(x)` is:

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