Labs / Mathematics
Polynomial Playground
Every polynomial is a story about where it crosses zero. Drag the round root markers along the x-axis, add or remove roots, and stack them up into double and triple roots — the curve, its turning points, and both algebraic forms redraw the instant you move.
f(x)= 0deg 3tails ↙ ↗
What to try
- Slide two roots until they land on the same spot. Why does the curve stop crossing the axis there and just kiss it instead?
- Bump a root's multiplicity to ×3. What happens to the curve as it passes through — does it flatten out?
- Drag the leading coefficient a from positive to negative. Which way do the two tails flip, and why do both ends move together?
- A degree-4 polynomial — how many turning points can it have at most, and how few? Can you make it have exactly one?
- With an odd degree, can you ever get both tails pointing the same way? What about with an even degree?