Easy question about exact results on screen

[PedroML]

Thank you in advance.
Trying to get zeros of this polinomy: x^3-x^2+0.5x-0.125, which settings allows me to get the exac form :1/2,(1+sqrt(3)*i)/4,(1-sqrt(3)*i)/4)??
The exact question would be, which settings bring the exact "answer" without decimals?


Thank you again!
Pedro ML

[Didier Lachieze]

To get exact results you need to use exact fractions for the numbers (for ex. 5/10) and not approximate decimal numbers such as 0.5
In CAS mode:

Code:

cSolve(x^3-x^2+(5/10)*x-(125/1000)=0,x)

will provide the exact result you're expecting.

[salvomic]

if you use (in CAS: in Home I get [] -why?- ...)
cZeros(x^3-x^2+(½)*x-(⅛))
you get
[\( \frac{1}{2} \ \frac{1}{4}*(\sqrt{3}*i+1) \ \frac{1}{4}*(-\sqrt{3}*i+1) \)]

As you know, If you input .05, .0125 you'll get only [0.5]

I'm using CAS and check in the "complex" and "exact" items in Shift-CAS Settings...

Salvo

[PedroML]

Thank you so much Salvo, Didier.
Both answers are great, and incredible fast!!!

Best regards!

[salvomic]

(06-01-2016 04:23 PM)PedroML Wrote:  Thank you so much Salvo, Didier.
Both answers are great, and incredible fast!!!

Best regards!

you're welcome :-)

also, Pedro, you can use (if you want) 0.5 and 1.125, and then, after getting the approx results, use QPI program (QPI by Han) to obtain the same symbolic results...

Hovewer, as Didier said, it's better use fractions instead of decimals for best results.

Salvo