Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

Find the number of polynomials P(x) with integer coefficients such that P^ (x)>0 and (P(x))^2+4 4 P (x^2 ) for all x .

Correct answer

Step-by-step solution

aligned & P^ (x)>0 and (P(x))^2+4 4 P (x^2 ) & Put x=0 (P(0))^2-4 P(0)+4 0 & (P(0)-2)^2 0 P(0)=2 & |||1y put x=1 (P(1)-2)^2 0 & P(1)=2 aligned Using Rolle's theorem in [0,1] P^ (c)=0 for some c (0,1) but given P^ (x)>0 . Hence no polynomials exists.

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