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AP EAMCET202422 May 2024Evening ShiftMathematicsQuadratic EquationActual

If ₁, ₂, ₃, ₄, ₅ are the roots of x^5-5 x^4+9 x^3-9 x^2+5 x-1=0 then 1 ₁^2 + 1 ₂^2 + 1 ₃^2 + 1 ₄^2 + 1 ₅^2 =

Options

  1. A15
  2. B1 7
  3. C7
  4. D12

Correct answer

C. 7

Step-by-step solution

x^5-5 x^4+9 x^3-9 x^2+5 x-1=0 ...(i) a₀ x^ n +a₁ x^ n -1 +a₂ x^ n -2 + .+a_ n -1 x+a_ n =0 Here a₀=-a_ n , a₁=-a_ n -1 is class II reciprocal equation. So, eq (i) is an odd degree reciprocal equation By inspection x=1 is a root Using synthetic division array c|cccccc 1 & 1 & -5 & 9 & -9 & 5 & -1 & 0 & 1 & -4 & 5 & -4 & 1 & 1 & -4 & 5 & -4 & 1 & 0 array x^4-4 x^3+5 x^2-4 x+1=0 ...(ii) Equation (ii) is an even degree reciprocal equation of class I. x^4-4 x^3+5 x^2-4 x+1 x^2 =0 (x^2+ 1 x^2 )-4 (x+ 1 x )+5=0 ....(iii)

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