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AP EAMCET202423 May 2024Morning ShiftMathematicsQuadratic EquationActual

The cubic equation whose roots are the squares of the roots of the equation 12 x^3-20 x^2+x+3=0 is

Options

  1. Ax^3+376 x^2-121 x-9=0
  2. B144 x^3-400 x^2+121 x+98=0
  3. C144 x^3-376 x^2+121 x-9=0
  4. Dx^3+400 x^2-121 x-98=0

Correct answer

C. 144 x^3-376 x^2+121 x-9=0

Step-by-step solution

Let , , be the roots of the equation aligned & 12 x^3-20 x^2+x+3=0 & + + = 20 12 & + + = 1 12 , = -3 12 aligned Now, ( + + )^2= ^2+ ^2+ ^2+2( + + ) aligned & array l ^2+ ^2+ ^2= 376 144 and, ( + + )^2=( )^2+( )^2+( )^2 +2 ( + + ) ( )^2+( )^2+( )^2= 121 144 array aligned Now, required equation is aligned & x^3- ( ^2+ ^2+ ^2 ) x^2+ ( ^2 ^2+ ^2 ^2+ ^2 ^2 ) x & 144 x^3-376 x^2+121 x-9=0 . aligned

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