Double Roots on the Casio 115 and 991 Series

[Matt Agajanian]

I’ve seen a video comparing a Casio 991EX Classwiz to a TI 36X Pro. One of the more interesting comparisons is in the aspect of multiple roots. Using the Polynomial Solver for a third-degree polynomial on both machines, the 36X Pro neatly and directly shows all roots, the first and the two double roots. The Casio only shows two results. It leaves you wondering which is the double root.

I’ve tried deflation to reveal all roots of the x^3-13x^2+51x-63=0 on the 991EX. I'll get 7 and 3 with a deflation method. When I use deflation for the third root, I get a ‘Can’t Solve’ error. So, you’re left wondering which is the double root.

Anyone got an alternative method to find double/identical multi-roots on the 115 and 991 series Casio models?

[klesl]

x^3-13x^2+51x-63=(x-7)(x-3)(x-a)
so by comparing the last term with multiplicated roots we get
-63=(-7)*(-3)*a
3=a
or by brute force
7*7*3=147
7*3*3=63

[Albert Chan]

(11-07-2023 10:39 AM)klesl Wrote:  x^3-13x^2+51x-63=(x-7)(x-3)(x-a)
so by comparing the last term with multiplicated roots we get -63=(-7)*(-3)*a

Another way, sum of roots = -a1/a0 --> missing root = 13 - 7 - 3 = 3
(not as accurate as using product of roots, but likely good enough)

BTW, if Casio return roots [x1,x2] only, it seems to mean [x1,x2,x2], i.e x3 = x2