ausmathgenius420
New member
- Joined
- Aug 5, 2021
- Messages
- 44
Hi,
The textbook question is: [imath]z^3+mz+52=0[/imath] and [imath]2+3i[/imath] is a solution, find m.
Steps to solve:
However both 4 and -4 satisfy the polynomial, giving a total of 4 solutions?
The textbook question is: [imath]z^3+mz+52=0[/imath] and [imath]2+3i[/imath] is a solution, find m.
Steps to solve:
- Conjugate theorem gives another solution (2-3i)
- Convert to factor of z (i.e. (z-(2+3i)) is a factor)
- Multiply both factors and long divide to give: the third factor [math]z+4 r. (m+3)z[/math]
- m must be -3 thus (so remainder =0) [imath]z^3-3z+52=0[/imath]
However both 4 and -4 satisfy the polynomial, giving a total of 4 solutions?