[size=85] Because one of the roots of the quintic polynomial is a [b]Real[/b] number, let's set it explicitly with a slider: [b][color=#980000]x0[/color][/b]. Thus the coefficient [b][color=#0000ff]a[sub]0[/sub][/color][/b] of this fifth degree polynomial is a function of [b][color=#980000]x0 [/color][/b](p(x0)). In the applet, you can use the sliders and corresponding buttons to approximate the desired value of [b][color=#0000ff]a[sub]0[/sub][/color][/b]. Using the [i][u][url=https://en.wikipedia.org/wiki/Ruffini%27s_rule][b]Ruffini rule[/b][/url][/u][/i], dividing the original polynomial by the binary one, we reduce the order of the polynomial to 4, the [u][i][url=https://www.geogebra.org/m/hsq2qqxe][b]solution[/b][/url][/i][/u] of which is known in symbolic formulas.[br] Roots, stationary and inflection points of quintic polynomial computed using symbolic solutions you will also find in the [url=https://www.geogebra.org/m/mhxk9tbc]applet[/url].[/size]