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If x³-2 x²-9 x+18=0 and A= | array lll 1 & 2 & 3 4 & x & 6 7 & 8 & 9 array | , then the maximum value of A is

Options

  1. A96
  2. B36
  3. C24
  4. D120

Correct answer

A. 96

Step-by-step solution

Given, x³-2 x²-9 x+18=0 and A= | array lll 1 & 2 & 3 4 & x & 6 7 & 8 & 9 array |x³-2 x²-9 x+18=0 x²(x-2)-9(x-2)=0 (x²-9 )(x-2)=0 (x-3)(x+3)(x-2)=0 x=2,3,-3A= | array lll 1 & 2 & 3 4 & x & 6 7 & 8 & 9 array |=1(9 x-48)-2(36-42)+3(32-7 x)=9 x-48+12+96-21 x=-12 x+60A( when x=2)=-12 2+60=36A( when x=3)=-12 3+60=24A( when x=-3)=-12 (-3)+60=96 More value of A at x=-3 is 96 .

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