Find a method by which one can compute the coefficients of from the roots of by performing not more than additions and multiplications.
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Find a method by which one can compute the coefficients of $P(x) = x^6 + a_1x^5 + \cdots+ a_6$ from the roots of $P(x) = 0$ by performing not more than $15$ additions and $15$ multiplications.
Izvor: Međunarodna matematička olimpijada, shortlist 1985
Školjka 
from the roots of 
by performing not more than 
additions and