If P(x) is a polynomial such thatP(x)+P(2x)=5×2−18 then limx→3 P(x)x−3 is

If P(x) is a polynomial such that

P(x)+P(2x)=5x218 then limx3P(x)x3 is

  1. A
  2. B
  3. C
  4. D

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    Solution:

    Clearly, P(x) is a quadratic polynomial. So, let

    P(x)=ax2+bx+c Then

    P(x)+P(2x)=5x218ax2+bx+c+4ax2+2bx+c=5x2185ax2+3bx+2c=5x2185a=5,3b=0 and 2c=18a=1,b=0 and c=9P(x)=x29

    and , Hence limx3P(x)x3=limx3x29x3=limx3(x+3)=6

     

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