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Equal Roots (Tomato subjective 70)

problem: Suppose that all roots of the polynomial equation
\({\displaystyle{x^4 – 4x^3 + ax^2 +bx + 1}} \) = 0 are positive real numbers.
Show that all the roots of the polynomial are equal.

solution: \({\displaystyle{x^4 – 4x^3 + ax^2 +bx + 1}} \) = 0
If the roots are \({\displaystyle{\alpha}} \), \({\displaystyle{\beta}} \), \({\displaystyle{\gamma}} \) and \({\displaystyle{\lambda}} \) .
then \({\displaystyle{\alpha}} \), \({\displaystyle{\beta}} \), \({\displaystyle{\gamma}} \) and \({\displaystyle{\lambda}} \) = 1
& \({\displaystyle{\alpha}} \) + \({\displaystyle{\beta}} \) + \({\displaystyle{\gamma}} \) + \({\displaystyle{\lambda}} \) = 4.

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September 24, 2015

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