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Problem

For a cubic polynomial $a_3 x^3 + a_2 x^2 + a_1 x + a_0$, the roots $r_1$, $r_2$, and $r_3$ come in three symmetric combinations: $\sigma_1 = r_1 + r_2 + r_3$, $\sigma_2 = r_1 r_2 + r_1 r_3 + r_2 r_3$, and $\sigma_3 = r_1 r_2 r_3$.

The sum of the $k^{\rm th}$ powers of the roots is defined as $s_k = r_1^k + r_2^k + r_3^k$.

With $s_1 = a$, $s_2 = b^2$, and $s_3 = a^3$, find the three roots in terms of $a$ and $b$.

Details
Contributer: Josh
Authors
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References
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Problem Sets This Problem Belongs to:
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VARIABLES
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DEFINITIONS
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