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AP EAMCET2011MathematicsQuadratic Equation

aligned & x^2+x+1 (x-1)(x-2)(x-3) = A x-1 + B x-2 + C x-3 & A+C= aligned

Options

  1. A4
  2. B5
  3. C6
  4. D8

Correct answer

D. 8

Step-by-step solution

Given, array r x^2+x+1 (x-1)(x-2)(x-3) = A x-1 + B x-2 + C x-3 array aligned x^2+x & +1=A(x-2)(x-3) & +B(x-1)(x-3)+C(x-1)(x-2) aligned Put x=1,2 and 3 respectively we get array lc & 1+1+1=A(1-2)(1-3) & 3=2 A A= 3 2 & 2^2+2+1=B(2-1)(2-3) & 7=-B B=-7 and & 3^2+3+1=C(3-1)(3-2) array array ll & 13=2 C C= 13 2 & A+C= 3 2 + 13 2 =8 array

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