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AP EAMCET201726 Apr 2017Morning ShiftMathematicsQuadratic EquationActual

If , , are the roots of x^3+p x^2+q x+r=0 , then the value of (1+ ^2 ) (1+ ^2 ) (1+ ^2 ) is

Options

  1. A(r-p)^2+(r-q)^2
  2. B(1+p)^2+(1+q)^2
  3. C(r+p)^2+(q+1)^2
  4. D(r-p)^2+(q-1)^2

Correct answer

D. (r-p)^2+(q-1)^2

Step-by-step solution

Given that , and are the roots of the equation x^3+p x^2+q x+r=0 aligned & Now, (1+ ^2 ) (1+ ^2 ) (1+ ^2 ) & = (1+ ^2 ) (1+ ^2+ ^2+( )^2 ) & =1+ ^2+ ^2+( )^2+ ^2+( )^2+( )^2+( )^2 & =1+ ( ^2+ ^2+ ^2 )+ (( )^2+( )^2+( )^2 . & =1+ [( )^2 . & + [( + + )^2-2( + + ) ]+( ( + + )]+( )^2 aligned From Eq. (i),(i i) and (iii), we get aligned & =1+ [p^2-2 q ]+ [q^2-2 r p ]+r^2 & =1+p^2-2 q+q^2-2 r p+r^2 & =(q-1)^2+(r-p)^2 aligned

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