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AP EAMCET202017 Sep 2020Evening ShiftMathematicsQuadratic EquationActual

Roots of the equation (x^3-3 x^2+3 x-9=0 ) are ......

Options

  1. A(3,1+2 , 1+2 ^2 )
  2. B(3,-1+2 ,-1-2 ^2 )
  3. C(3,2- , 2- ^2 )
  4. D(1,1+2 , 1+2 ^2 )

Correct answer

A. (3,1+2 , 1+2 ^2 )

Step-by-step solution

Given equation is, ( aligned & x^3-3 x^2+3 x-9 & =0 & (x-3) (x^2+3 ) & =0 aligned ) So one of root is 3 . Now, (x^2+3=0 ) taking (x=1+2 w ), we have ( aligned (1+2 )^2 & +3 & =1+4 ^2+4 +3 & =1+ (4 ^2+4 +4 )-1 & =1+4 ( ^2+ +1 )-1 & =0 ; or ^2+ +1=0 aligned ) Similarly, (1+2 ^2 ) also satisfies given equation So roots are; (3,1+2 ) and (1+2 ^2 )

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