How do you solve #a^4 + 2a^3 + a^2=0#?

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Answer 1 · 2016-04-07T10:12:30

#a = 0# or #a = -1#

By factoring:

#a^4+2a^3+a^2 = 0#

#=> a^2(a^2+2a+1) = 0#

#=> a^2(a+1)^2 = 0#

#=> a^2 = 0# or #(a+1)^2 = 0#

#=> a = 0# or #a+1 = 0#

#:. a = 0# or #a = -1#