SOLUTION: Find the 4 roots of the equation: x^4+kx^2+1=0 k^2<4

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the 4 roots of the equation: x^4+kx^2+1=0 k^2<4      Log On


   

Question 67434: Find the 4 roots of the equation:
x^4+kx^2+1=0
k^2<4
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
figure that p = x^2 for now:
(x^2)^2 + k(x^2) + 1 = 0
p^2 + kp + 1 = 0
p^2 + kp = -1
(p + k/2)^2 = -1 + k^2/4
p + k/2 = +- sqrt(k^2/4 - 1)
p = -k/2 +- sqrt(k^2/4 - 1)
x^2 = -k/2 +- sqrt(k^2/4 - 1)
x = +- sqrt(-k/2 +- sqrt(k^2/4 - 1))
~~~~~~
k^2 < 4
-2 < k < 2