Algebraic numbers: if a, b are roots of x^5+x+1=0,x^5+2x+1=0, what is min. polynom fo

[icegood]

Hi there. Where can i read that algebraic numbers (i. e. those one which are root of polynom with integer coefficients) are closed under addition and multiplication?
In particular, if we have two reals a and b which are roots of :

x^5+x+1=0
x^5+2*x+1=0

then what minimal polynom will be for a+b?

 

[Ishuda]

Hi there. Where can i read that algebraic numbers (i. e. those one which are root of polynom with integer coefficients) are closed under addition and multiplication?
In particular, if we have two reals a and b which are roots of :

x^5+x+1=0
x^5+2*x+1=0

then what minimal polynom will be for a+b?

Cribbing an answer from one of our Elite Members here:

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