JEE Main2012MathematicsQuadratic EquationActual

If the sum of the square of the roots of the equation x^2-( -2) x-(1+ )=0 is least, then is equal to

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Correct answer

D. 2

Step-by-step solution

Given equation is x^2-( -2) x-(1+ )=0 Let x₁ and x₂ be two roots of quadratic equation. aligned & x₁+x₂= -2 and x₁ x₂=-(1+ ) & (x₁+x₂ )^2=( -2)^2= ^2 +4-4 aligned aligned & x₁^2+x₂^2= ^2 +4-4 -2 x₁ x₂ & = ^2 +4-4 +2(1+ ) & = ^2 -2 +6 aligned Now, By putting = 6 , = 4 , = 3 and = 2 in (A) one by one We get least value of x₁^2+x₂^2 at 2 Hence, = 2

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