Quartics
A quartic is a polynomial
of degree 4. The polynomial may factorise with between one and four factors, some of which may be repeated. The different cases are
1. four distinct linear real factors :
2. a squared real linear factor and two different real linear factors :
3. two squared real linear factors:
4. a cubed factor and one real linear factor :
5. a real linear factor raised to the fourth power:
6. one real quadratic factor with
and two real linear factors :
7. two real quadratic factors each with
If the coefficient of
is positive the graph tends to infinity as
Ifis fully factorised into real linear factors, then
For a distinct factor graph cuts the x - axis at |
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For each squared factor graph touches the x - axis at |
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If graph cuts the x - axis at |
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If the graph touches the x - axis but is a minimum at that point. |
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If a quartic with quadratic factor with have |
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If a quartic with quadratic factors both with we have |
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the
the
the
and has a point of inflecion at
has one real
