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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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