Find a method by which one can compute the coefficients of
![P(x) = x^6 + a_1x^5 + \cdots+ a_6](/media/m/f/2/c/f2c1c83f76b2a7e5739fe0014133300d.png)
from the roots of
![P(x) = 0](/media/m/3/c/5/3c5500514ff4e96c943ccbcf3b41d1e8.png)
by performing not more than
![15](/media/m/8/f/3/8f3c9ff2c5f5085be88380fc85a87f7d.png)
additions and
![15](/media/m/8/f/3/8f3c9ff2c5f5085be88380fc85a87f7d.png)
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.