what-are-the-reasons-for-not-using-x-2c-b-b-2-4ac-as-the-quadratic-formula-i-proved-it-

Question Number 93730 by Rio Michael last updated on 14/May/20

what are the reasons for not using

x = \frac{2 c}{- b \pm \sqrt{b^{2} - 4 a c}} as the quadratic formula ?

i proved it .

Commented by Rasheed.Sindhi last updated on 14/May/20

\frac{2 c}{- b \pm \sqrt{b^{2} - 4 a c}}

= \frac{2 c}{- b \pm \sqrt{b^{2} - 4 a c}} \times \frac{- b \mp \sqrt{b^{2} - 4 a c}}{- b \mp \sqrt{b^{2} - 4 a c}}

= \frac{2 c (- b \mp \sqrt{b^{2} - 4 a c})}{b^{2} - (b^{2} - 4 a c)}

= \frac{2 c (- b \mp \sqrt{b^{2} - 4 a c})}{4 a c}

= \frac{- b \mp \sqrt{b^{2} - 4 a c}}{2 a}

= \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

∴ Y o u r f o r m u l a i s e q u i v a l e n t t o

t h e q u a d r a t i c {f o r m u l a}^{∙}

B u t t h e q u a d r a t i c {f o r m u l a}^{∙} i s b e t t e r

s i m p l i f i e d f o r m b e c a u s e i t {d o e s n}^{'} t

c o n t a i n r a d i c a l i n d e n o m i n a t o r .

^{∙} H e r e^{'} t h e q u a d r a t i c {f o r m u l a}^{'} m e a n s :

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

Commented by mr W last updated on 14/May/20

f o r t h e s a m e r e a s o n w h y y o u w r i t e

\frac{\sqrt{2}}{2}, n o t \frac{1}{\sqrt{2}}, a n d 2 + \sqrt{3}, n o t \frac{1}{2 - \sqrt{3}} .

Commented by Rio Michael last updated on 14/May/20

okay sirs thank you, was just wondering why

this formula is so negleted