Cubic function : Roots[f] Search

lewws shared this problem 2 years ago
Not a Problem

Hi,

A student and I were trying to find roots of f(x) = x³ + (k - 6) x² + (2k - 1) x + 30 by varying k on a slider, and using Roots(f).

One of the expected roots is x = -2 since (x+2) is always a factor of f(x) regardless of values of k.

But remaining 2 roots of cubic function depend on values of k.


We were trying to find the repeated root. We set system to 12 decimal places trying to get as close to the repeated root as possible, by varying k and observing the graph

Near to the repeated root we unexpectedly found 4 roots instead of 3. Can we check if there's some algorithm weakness in the system in using Roots[] to find the roots?


Regards.

lewws


43168be35858ced349dc45f89e9a8758

Comments (4)

photo
1

You can solve it in CAS. A 3rd degree function with 4roots...???

chris

925a10d9b3ac9cefdc60452a65178ede

photo
1

Thanks Chris!

photo
photo
1

use root(polynomial) instead roots(function,startx,endx)

the numerical methods are less accuracy

And I could not repeat your issue

photo
1

Thanks too, mathmagic.

© 2022 International GeoGebra Institute