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AP EAMCET2010MathematicsQuadratic Equation

Let 1 be a real root of the equation x^3-a x^2+a x-1=0 , where a -1 is a rea number. Then, a root of this equation, among the following, is

Options

  1. A^2
  2. B- 1
  3. C1
  4. D- 1 ^2

Correct answer

C. 1

Step-by-step solution

Equation x^3-a x^2+a x-1=0 and 1 , a -1 . we put, (x= 1 y ) in given equation Then, ( 1 y )^3-a ( 1 y )^2+a ( 1 y )-1=0 1 y^3 - a^2 y^2 + a y -1=01-a^2 y+a y^2-y^3=0 y^3-a y^2+a^2 y-1=0 Since, the reduced equation is same as original equation by replacing (x= 1 y ) i e , reciprocal root of the given equation. Hence, (x= 1 ) is a root of the given equation

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