SOLUTION: What is the fundamental difference between even roots and odd roots?

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: What is the fundamental difference between even roots and odd roots?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 423861: What is the fundamental difference between even roots and odd roots?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Recall that x-intercepts are another name for the roots or zeroes of a polynomial.
generally a root is termed " even " if it is a root an even number of times...similarly for " odd "
f%28x%29+=+%28+x%2B+5%29%5E4+%28+x+-6%29+%5E3 has -5 as an even root and 6 as an odd root
at "even " roots the graph touches but does not cross the domain axis..." odd " implies crossing
or
If a root has an even multiplicity, the graph will bounce+off the axis, as with the graph of y=x%5E2. If a root has an odd+multiplicity, the graph will pass+through the axis, as with the graph of y=x%5E3.