Degree of polynomial in one variable having 4 terms can not be:
Answers
Answer:
Fourth degree polynomials are also known as quartic polynomials. Quartics have these characteristics:
Zero to four roots.
One, two or three extrema.
Zero, one or two inflection points.
No general symmetry.
It takes five points or five pieces of information to describe a quartic function.
Roots are solvable by radicals. (Very advanced and complicated.)
Number of Roots
Notes
Click for example
0, 1, 2, 3, 4
3
2
Roots of first and second derivatives are all different. Line symmetric.
Graph 1
0, 1, 2, 3, 4
3
2
Roots of first and second derivatives are all different. Not symmetric.
Graph 2
3
1
Not possible.
3
0
Not possible.
0, 1, 2
2
2
One extremum. One root of first derivative equals one root of second.
Graph 3
2
1
Not possible.
2
0
Not possible.
0, 1, 2
1
2
Roots of first and second derivatives are all different.
Graph 4
0, 1, 2
1
1
Does not have a true inflection point.
Graph 5
0, 1, 2
1
1
Does not have a true inflection point. Line symmetric.
Graph 6
0, 1, 2
1
0
Generally asymmetric.
Graph 7