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The roots of a certain quartic satisfy the following: a + b + c + d = 5 a 3 + b 3 + c

The roots of a certain quartic satisfy the following:

a + b + c + d = 5 a3 + b3 + c3 + d3 = 35

a2 + b2 + c2 + d2 = 15 a4 + b4 + c4 + d4 = 99

Find the quartic and its roots.

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