How do you find the complex roots of #x^4-10x^2+9=0#?

1 Answer
Jan 10, 2017

Answer:

The roots are #+-3# and #+-1#

Explanation:

Note that #9+1 = 10# and #9*1 = 9#.

Hence we find:

#0 = x^4-10x^2+9#

#color(white)(0) = (x^2-9)(x^2-1)#

#color(white)(0) = (x^2-3^2)(x^2-1^2)#

#color(white)(0) = (x-3)(x+3)(x-1)(x+1)#

So the four roots of this quartic equation are #+-3# and #+-1#

These are Real numbers, but any Real number is also a Complex number (of the form #a+0i# if you wish).