x^8 - x^4 - 240 = 0
Consider all of the (possibly complex) roots to this equation. How many of them have a positive real part?
Define y = x^4
y^2 - y - 240 = 0
y = (1 +/- sqrt(1+960)) / 2 = -15 or 16
x^4 = 16 has roots of 2, -2, 2i and -2i, only one of which has a positive real part.
x^4 = - 15 has roots 15^(1/4)/sqrt(2) times choice of:
1+i, -1+i, -1-i and 1-i
Two of these have positive real parts.
All together the equation has 3 roots with positive real parts, 3 with negative real parts and 2 with real part of zero.
|
|
Posted by Charlie
on 2016-10-16 11:13:54 |
solution