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AP EAMCET201921 Apr 2019Morning ShiftMathematicsQuadratic EquationActual

If , , are the roots of x^3-6 x^2+11 x-6=0 , then the equation having the roots ^2+ ^2, ^2+ ^2 and ^2+ ^2 is

Options

  1. Ax^3-28 x^2+245 x-650=0
  2. Bx^3-28 x^2+245 x+650=0
  3. Cx^3+28 x^2-245 x-650=0
  4. Dx^3+28 x^2+245 x-650=0

Correct answer

A. x^3-28 x^2+245 x-650=0

Step-by-step solution

aligned & x^3-6 x^2+11 x-6=0 & (x-1)(x-2)(x-3)=0 & x=1,2,3 aligned , , are the roots of the Eq.(i), so =1, =2, =3 Therefore, ^2+ ^2=(1)^2+(2)^2=5= ^ (say) ^2+ ^2=(2)^2+(3)^2=13= ^ ( say ) and ^2+ ^2=(3)^2+1=10= ^ (say) Equation of the having the roots ^ , ^ and ^ , aligned & x^3- ( ^ + ^ + ^ ) x^2+ ( ^ ^ + ^ ^ + ^ ^ ) x & - ^ ^ ^ =0 & x^3-(5+13+10) x^2+(5 13+13 10+10 5) x & -5 13 10=0 & x^3-28 x^2+245 x-650=0 & aligned

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