Question 113943: I have one more question I need help with. I need to prove that the polynomial P(x)=x^3-3x^2-5 must have complex roots without using a graph and explain what rule can be used. I answered Descartes rule but my instructor is asking me to explain what this shows and what conclusion I can draw knowing number of roots for a cubic. This section has been a little tough for me. Any help would be much appreciated.
Thank you,
Lucy
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Well I'm assuming that you found that there is at most one positive real root using Descartes' Rule of Signs right? Now using this info, you can find the number of complex roots. Remember, a cubic will have 3 roots (either all real or one real and 2 complex). In fact, any polynomial of degree "n" will have n roots according to the Fundamental Theorem of Algebra. Since we have one real zero, we know that there must be 2 complex roots (complex roots always come in pairs).
|
|
|
