For what values of #m# does #z^3+(3+i)z^2-3z-(m+i) = 0# have at least one real root?
2 Answers
See below.
Explanation:
A possible solution is for
NOTE
If
Now making
hence
Explanation:
Given:
#z^3+(3+i)z^2-3z-(m+i) = 0#
Find values of
Assuming we are looking for suitable real values of
#z^2-1 = 0#
So:
#z = +-1#
If
#0 = z^3+(3+i)z^2-3z-(m+i)#
#color(white)(0) = 1+3+i-3-m-i#
#color(white)(0) = 1-m" "rarr" "m = 1#
If
#0 = z^3+(3+i)z^2-3z-(m+i)#
#color(white)(0) = -1+3+i+3-m-i#
#color(white)(0) = 5-m" "rarr" "m = 5#