new way to make quadratic equations easy

[C.Ret]

(08-04-2021 04:57 AM)Benjer Wrote:  I was surprised to learn that roots for quadratic equations could be solved using a slide rule, described in the manual for the Post Versalog:

I was also really surprise, so I grasp my father's Graphoplex REITZ n°620 and it's very short manual where no mention about how to solve a quadratic equation is present. So I reinserted this manual in the red cardboard box and try the two examples.

Here is a capture for the resolution of the first example : \( x^2+10x+15=0 \) . The trick is to mentally add value form the CI and the D scale. I get a hard time to found at which position I have to start seeking. To help me, I move the hairline (the middle hairline in red) to look for a sum as close as 10 as possible. Finally, the position of the middle hairline indicate the two roots on the CI and D scale respectively.

[attachment=9708]

(Note: the HP-15C armed with quadratic solving code is only showing one root at a time).

For the second example of equation \( x^2–12.2x-17.2=0 \), I check with an HP Prime to have the two roots on the display. I only realize after a few attempts, that since there is no CIF and DF scale on this slide rule I need to use the right index of CI set on 17.2 on the D scale. Then, the procedure is usingthe D and CI scales but the substraction have to match 12.2 as close as possible.

[attachment=9709]


P.S.: Please note that on this slide rule, scale CI and D have respectively black B and red a labels (original Graphoplex: French Règle à Calculs).

EDIT:
Is that a new way to make the quadratic equation solving esay ?
- new ? With a slide rule from 1958 ?
- easy ? scanning for adding or substrating values on D and CI scale ?