SOLUTION: How do I find all of the roots for x to the 4- 6x squared plus 7

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: How do I find all of the roots for x to the 4- 6x squared plus 7      Log On


   

Question 830419: How do I find all of the roots for x to the 4- 6x squared plus 7
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Substitute u=x%5E2
x%5E4-6x%5E2%2B7=0
u%5E2-6u%2B7=0
%28u-7%29%28u%2B1%29=0
Now back substitute,
u-7=0
x%5E2-7=0
x=sqrt%287%29 and x=-sqrt%287%29
.
.
u%2B1=0
u=-1
x%5E2=-1
x=i and x=-i