Question

Are all solutions that are negative in a quadratic formula an extraneous solution?

Answer 1

with a negative discriminant you mean? that means an imaginary solution then... but it will work in the original equation in most of the cases.

Answer 2

\(\normalsize\color{ slate }{\Huge{\bbox[5pt, lightcyan ,border:2px solid black ]{ \LARGE{x=~} \huge{ \frac{-\color{magenta}{b} \pm\sqrt{ \color{magenta}{b} ^2-4 \color{blue}{a} \color{red}{c}}}{2 \color{blue}{a}} }~ }}}\) and if: \(\LARGE\color{black}{ (\color{magenta}{b} ^2-4 \color{blue}{a} \color{red}{c})<0 }\)

Answer 3

this box disconnected me...

and if \(\LARGE\color{black}{ (\color{magenta}{b} ^2-4 \color{blue}{a} \color{red}{c})<0 }\) the the solutions are imgainry