1.

Consider the equation x^(5) + 5lambdax^(4) -x^(2) + (lambdaalpha-4)x^(2) - (8lambda +3) x +(lambdaalpha-2)=0, where lambda, alpha in R (i) Determine a such that the given equation has exactly one root independent of lambda. (ii) Determine a such that the given equation has exactly two roots independent of lambda .

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ANSWER :(i) `ALPHA =-64/5`


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