Roots of Quintic polynomial computed using symbolic solutions. 1
Because one of the roots of the quintic polynomial is a Real number, let's set it explicitly with a slider: x0. Thus the coefficient a0 of this fifth degree polynomial is a function of x0 (p(x0)). In the applet, you can use the sliders and corresponding buttons to approximate the desired value of a0. Using the Ruffini rule, dividing the original polynomial by the binary one, we reduce the order of the polynomial to 4, the solution of which is known in symbolic formulas.
Roots, stationary and inflection points of quintic polynomial computed using symbolic solutions you will also find in the applet.