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Question

Determine positive values of a such that x211x+a and x214x+2a may have a common factor.

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Solution

let common root be α
so α will satisfy both the equations
α211α+a=01α214α+2a=02213α+a=0α=a3putα=a3ineq1a2911a3+a=03a233a+9a=0a224a=0a=0or24
ubt positive value of a is 24

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