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The biquadratic equation, two of whose roots are 1+i, 1- 2 , is

Options

  1. Ax^4-4 x^3+5 x^2-2 x-2=0
  2. Bx^4+4 x^3-5 x^2+2 x+2=0
  3. Cx^4+4 x^3-5 x^2+2 x-2=0
  4. Dx^4+4 x^3+5 x^2-2 x+2=0

Correct answer

A. x^4-4 x^3+5 x^2-2 x-2=0

Step-by-step solution

When 1+i, 1-i are the roots, then Sum of the roots =1+i+1-i=2 and product of the roots =1+1=2 The equation is x^2-2 x+2=0 When 1- 2 , 1+ 2 are the roots, then Sum of the roots =1- 2 +1+ 2 =2 Product of the roots =1-2=-1 The equation is x^2-2 x-1=0 The bi-quadratic equation is array r (x^2-2 x+2 ) (x^2-2 x-1 )=0 (x^4-(2+2) x^3=(-1+4+2) x^2 . =(2-4) x-2=0 x^4-4 x^3+5 x^2-2 x-2=0 array

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