Paragraph: Consider the equation x^4+2 a x^3+x^2+2 a x+1=0 , where a R . Also, range of f(x)=x+ 1 x is (- ,-2] [2, ) Question: If equation has at least two distinct positive real roots, then all possible values of 'a' are

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Correct answer: A. (- ,- 1 4 )

(x+ 1 x )^2+2 a (x+ 1 x )-1=0 (1) t^2+2 a t-1=0 (2) t 2 and t -2 (Given) Equation (1) will have at least two positive roots, when at least one root of equation (2) will be greater than 2

Paragraph: Consider the equation x^4+2 a x^3+x^2+2 a x+1=0 , where a R . Also, range of f(x)=x+ 1 x is (- ,-2] [2, ) Question: If equation has at least two distinct positive real roots, then all possible values of 'a' are

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