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AP EAMCET2008MathematicsQuadratic Equation

The cubic equation whose roots are thrice to each of the roots of x^3+2 x^2-4 x+1=0 is

Options

  1. Ax^3-6 x^2+36 x+27=0
  2. Bx^3+6 x^2+36 x+27=0
  3. Cx^3-6 x^2-36 x+27=0
  4. Dx^3+6 x^2-36 x+27=0

Correct answer

D. x^3+6 x^2-36 x+27=0

Step-by-step solution

Given equation is x^3+2 x^2-4 x+1=0 Let , and be the roots of the given equation aligned & + + & =-2, + + =-4 and & & =-1 aligned Let the required cubic equation has the roots 3 , 3 and 3 . aligned 3 +3 +3 & =-6 3 3 +3 3 +3 3 & =-36 3 3 3 & =-27 aligned Required equation is aligned x^3-(-6) x^2+(-36) x-(-27) & =0 x^3+6 x^2-36 x+27 & =0 aligned

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