The degree n of the polynomial P(x)
(corresponding to the number of
x-intercepts in the graph of y=P(x),
counting multiplicity)
can be changed using the "+"
and "-" buttons
under the label marked "n=". Each time the degree
is changed, the values of the leading coefficient and
roots are set to default values depending
on the new degree.
The roots can be changed in either of two ways:
Clicking and dragging the
red dots on the graph.
Entering values for any of the roots c_{1}
to c_{n} directly into the text input fields marked
"c_{1}=",
"c_{2}=", etc.
The leading coefficient a_{n} (which is not affected by
the roots of the polynomial) can be changed by entering a value into
the text input field marked
"a_{n}="
(the displayed value of n changes with the degree of the polynomial).
Clicking the "Clear" button sets the
values of n, c_{1}, c_{2}, etc.,
to default values (n=2,
c_{1}=-1, c_{2}=1, other c_{i}
blank) and redraws the graph.
The text input fields for the leading coefficient a_{n}
and for the roots
c_{1} to c_{n} accept any decimal number.
The buttons under the graph
allow various manipulations of
the graph coordinates.
Examples
Other Notes
The labels marked
"a_{0}=",
"a_{1}=", etc.,
show the values of the coeficients
a_{0},
a_{1}, etc., of the polynomial P(x)
when multiplied out. As the roots c_{i} change,
the values of the coefficients a_{i} are updated
automatically.
Multiple roots can be explored by making
the values of two or more of the roots equal.
Note however that irreducible quadratic factors of polynomials, which
yield complex roots, are not supported by this applet.