Problem with 2nd order polynomial

[C.Ret]

(09-19-2024 06:16 PM)Liamtoh Resu Wrote:  How can the estimates for x be obtained without running proot first?

That's an excellent question. The only answer I know is that it's impossible unless you use divination magic.

There are no estimates because these are more precisely the limits of an interval. Only one estimate can be given to the solve instruction.

I have to apologize to you because I just realized that I left the 5-digits rounding that I usually use to make the captures.

In reality, I used the exact values ​​of a,b and c given by ktomb (at least the closest representation the HP Prime is able, since the numeric values he gives are far more precise that possible on an HP Prime).

Between the two captures these three values a,b and c ​​were simply divided by 10,000,000. Which means that it does not change the position of the roots of the quadratic polynomial \(a\cdot x^2 + b\cdot x + c \).
On the other hand, it has a non-negligible effect on the amplitude of all non-zero values of this quadratic.

This simple difference seems to dramatically change the operation of the solve instruction. But not if we give an estimate or a search interval.


If I were asked for advice, I would strongly recommend that any experienced HP Prime user to use the two modes HOME and CAS wisely.
* HOME mode for numerical calculations and resolutions only.
* CAS mode for symbolic calculations only.

The two screenshots below attempt to illustrate what I think would be a better use of the facetious HP Prime:

( I took care to use the STANDARD display mode even if I find it a bit stupid to have such long numbers with so many digits that make no sense. )

On the left, the HOME mode gives the numerical results immediately and without detour.
On the right, the CAS mode naturally gives an exact symbolic answer. Eventually, that symbolic answer may be exploited numerically.

Most often, incidents occur when one tries to obtain a solution that is simultaneously symbolic and numerical. These are two different realities, two philosophies that turn their backs on each other, two faces of the same mirror...