(0,1) (1,3) (2,9) (3,27) is the relationship linear,exponential, or neither
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Using the quadratic formula, we solve for .
Taking square roots on both sides, we end up with
Compute the square roots of -171 + 140i.
By de Moivre's theorem,
and the other root is its negative, -5 - 14i. We use the fact that (140, 171, 221) is a Pythagorean triple to quickly find
as well as the fact that
(whose signs are positive because of the domain of ).
This leaves us with
Compute the square roots of 5 + 12i.
By de Moivre,
and its negative, -3 - 2i. We use similar reasoning as before:
Lastly, compute the roots of -2i.
as well as -1 + i.
So our simplified solutions to the quartic are