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AP EAMCET2009MathematicsQuadratic Equation

If , , are the roots of x^3+4 x+1=0 , then the equation whose roots are ^2 + , ^2 + , ^2 + is

Options

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

Correct answer

C. x^3+4 x-1=0

Step-by-step solution

Given, , and are the roots of aligned & x^3+4 x+1=0 . & aligned & + + =0, + + =4, =-1 & Now, ^2 + + ^2 + + ^2 + = ^2 - + ^2 - + ^2 - &=-( + + )=0 aligned & ^2 ^2 ( + )( + ) + ^2 ^2 ( + )( + ) + ^2 ^2 ( + )( + ) aligned aligned = + + & =4 and ^2 ^2 ^2 ( + )( + )( + ) & =- =1 & ( + + =0) aligned Required equation is x^3+4 x-1=0

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