Mathematician Finds Easier Way to Solve Quadratic Equations

[Rolief_Rechner]

(04-27-2024 10:50 AM)Thomas Klemm Wrote:  

(04-26-2024 09:25 PM)Rolief_Rechner Wrote:  A consolation is you are not the first to do this.

I'm not sure I understand you correctly, but your QuadForm.pdf attachment uses the following incorrect formula:

\(
\begin{align}
x_{1,2} = - \frac{b}{a} \pm \sqrt{\left(\frac{b}{a}\right)^2 - \frac{c}{a}}
\end{align}
\)

This led to my comment.

Example

\(
\begin{align}
a &:= 1 \\
b &:= -5 \\
c &:= 6 \\
\\
x_{1,2} &= 5 \pm \sqrt{19} \\
\\
x_1 &\approx 0.641101 \\
x_2 &\approx 9.3589 \\
\end{align}
\)

\(\Rightarrow\) Incorrect

---

BTW: The proper way to quote a post is using the button:

(04-26-2024 06:01 AM)Thomas Klemm Wrote:  PS: You missed a factor 2 in the denominator.

The formula is derived by completing the square.
It was checked with Wolfram Alpha, attached.
If you still insist this is wrong, remedial education is suggested.