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AP EAMCET201824 Apr 2018Morning ShiftMathematicsQuadratic EquationActual

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

Options

  1. A-1, 1 3
  2. B3 5 2
  3. C1 i 3 2
  4. D1,- 1 3

Correct answer

A. -1, 1 3

Step-by-step solution

Given equation, x^5-5 x^4+9 x^3-9 x^2+5 x-1=0 x=1 is one root of equation. So, (x-1) (x^4-4 x^3+5 x^2-4 x+1 )=0 x^4-4 x^3+5 x^2-4 x+1=0 On dividing by x^2 , we get, aligned & x^2-4 x+5- 4 x + 1 x^2 =0 & (x^2+ 1 x^2 )-4 (x+ 1 x )+5=0 & (x+ 1 x )^2-4 (x+ 1 x )+3=0 & [ as x^2+ 1 x^2 = (x+ 1 x )^2-2 ] aligned Now, let x+ 1 x =y aligned y^2-4 y+3 & =0 (y-1)(y-3) & =0 y & =1,3 x+ 1 x =1 and x+ 1 x & =3 . & x^2+1=x and x^2+1=3 x & aligned Equation x^2-3 x+1=0 gives irrational roots Let , are roots then, aligned & + =3, =1

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