Substitute x = i t where t is assumed to be real:
t^4 - 3it^3 - 7t^2 -6 i t - 13 = 0
Take the imaginary part of the equation:
t^3 + 2 t = 0 --->
t(t^2 + 2) = 0
Now, we can see from the original equation for t that t = 0 is not a solution (this is actually implied by the real part of the equation). Since t has to be real, the equation:
t^2 + 2 = 0
cannot be satisfied.
Therefore the equation has no imaginary solutions.
State the possible number of imaginary zeros of g(x)= x4 + 3x3 + 7x2 - 6x - 13.
I came up with the answer of 2,4 or 0.
Is this correct?
Thanks for your help.
1 answer