Symmetric function of the root

[vijay1965]

if alpha, beta, gama and delta are the roots of x^4+px^3+qx^2+rx+s=0, find the value of alpha/beta + beta/alpha

 

[Dr.Peterson]

Why do you think this can be done?

There are four roots; a function of only two of them is not a symmetric function of all the roots, and can change according to which two roots you call alpha and beta.

 

[Otis]

Hi vijay. Each of the roots looks like this one. Are expressions like that what you expect to work with?

 

[vijay1965]

But sir, how to find the value of alpha/beta + beta/alpha. What is alpha and beta in this question?

 

[Otis]

… What is alpha and beta in this question?

Alpha and beta are roots of the 4th-degree polynomial that you posted. We cannot say which two roots the author calls alpha and beta. Can you ask the author?

The expression that I posted might be alpha, or beta, or gamma, or delta. But, my question to you is, "Are you prepared to work with two expressions like that?" If you are not, then maybe your materials contain a mistake or omission (or you've misinterpreted something).

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