How do you find the complex roots of #a^3+2a^2-8a=0#?

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Answer 1 · 2017-06-28T14:52:44

See below.

We can see that all of the variables have an #a#, so we can factor this out immediately.

#a(a^2+2a-8)=0#

So, one solution is #a=0#. The other solutions pertain to the quadratic, which we can find using factoring.

#a^2+2a-8=0#

#a^2-2a+4a-8=0#

#a(a-2)+4(a-2)=0#

#(a+4)(a-2)=0#

So,

#a=2,-4,0#, and there are no complex roots.