Roots of Polynomials
Graphs a polynomial function P
with given real roots, showing the
the roots and the coefficients of the polynomial.
How to use
How to use
The text input fields for the leading coefficient an
and for the roots
c1 to cn accept any decimal number.
The buttons under the graph
allow various manipulations of
the graph coordinates.
- The degree n of the polynomial P(x)
(corresponding to the number of
x-intercepts in the graph of y=P(x),
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 c1
to cn directly into the text input fields marked
- The leading coefficient an (which is not affected by
the roots of the polynomial) can be changed by entering a value into
the text input field marked
(the displayed value of n changes with the degree of the polynomial).
- Clicking the "Clear" button sets the
values of n, c1, c2, etc.,
to default values (n=2,
c1=-1, c2=1, other ci
blank) and redraws the graph.
The labels marked
show the values of the coeficients
a1, etc., of the polynomial P(x)
when multiplied out. As the roots ci change,
the values of the coefficients ai are updated
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.