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Finding solutions of complex equations

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squance:
Find all the solutions of the following equation.

z^4 -5z^2 -8z - 12 =0

I don't know how to do this one but the answerss are 3, -2, -1/2 + (i sqrt7)/
2, -1/2 - (i sqrt7)/2

Some help would be appreciated! :)

ell:
Hmm - there's probably a better and easier way than this, but you could let , then find when by substituting values like 1, 2, 3 and -1, -2, -3 etc.. (works out that and are factors)

Then use long division and divide by to obtain

Then, using long division again, divide by to obtain

You can complete the square on the quadratic:











Which means:



Then find the solutions for z from there. :)

squance:
Thanks ell!

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