Multiple (possibly complex) roots?

[Thomas Klemm]

(04-21-2014 01:20 AM)unfrostedpoptart Wrote:  On the HP/WP, which root does it normally pick?

It usualy picks the root with the smallest argument. Thus the WP-34S returns -2 for \(\sqrt[3]{ -8}\) but returns \(1+i\sqrt{3}\) when using [CPX] \(\sqrt[3]{-8+i0}\).

Quote:I assume to get all of them, I'd have to use SLV with different starting points.

When using Newton's method the choice of the starting point is crucial. The basin of attraction (the set of initial points that converge to the same root) for each root is a fractal:

Make sure to start in the vicinity of one of them.

I'm afraid that SLV can't be used to find complex roots. For polynomials with real coefficients you could use Bairstow's Method.

Cheers
Thomas