For polynomial equations of degree < 5 see here.
An engineering problem (related to airplane engines) involves solving (with respect to x)
x^6 - 27*x^5 + 105*x^4 - 104*x^3 + 81*x^2 - 21*x + 2 = 0
We can draw the graph with JavaScript; for example by this script:
I understand that there is a solution between 0 and 10 and there is another between 10 and 25.
By using
equp2.htm:
The solutions are 3.44432622220982 and 22.53916874388888 (but we can be satisfied with a smaller number of digits).
We could do without drawing the graph. We could identify the initial intervals in which the solutions fall by using the [test] button.
[the problem is taken from "Science with Pocket Calculators" by David R. Green, John L. Lewis (1978)]
The script can also be used to tabulate polynomials. For example, in the case of the same function F considered above we have that
