Question

how do I find the complex roots of the function

x^4 + 7x^2 + 6 = 0

Answer 1

use the quadratic formula to solve for
\(x^2\) then take the square root of your answers

Answer 2

actually this one factors as
\[(x^2+6)(x^2+1)=0\]

Answer 3

so just forget about the x^4 and plug the rest in to the quadratic equation?

Answer 4

telling you
\[x^2=-6\implies x=\pm\sqrt{6}i\] or
\[x^2=-1\implies x=\pm i\]

Answer 5

if it did not factor so easily, you would use the quadratic formula, yes

Answer 6

You factored it just by intuition or what?