How do you solve the quadratic using the quadratic formula given x4+13x2+36=0 over the set of complex numbers?

1 Answer
Feb 15, 2017

±2iand±3i

Explanation:

x4+13x2+36=0

assuming y=x2,

(x2)2+13x2+6=y2+13y+36=0

using y=b±b24ac2a, where a=1,b=13andc=36

y=13±1324(1)(36)2(1)

y=13±1691442

y=13±252

y=13±52

y=13+52=4, y=1352=9

when y=4,x2=4

x=4=4(1)=41=±2i

when y=9,x2=9

x=9=9(1)=91=±3i