what are the reasons for not using x = ((2c)/(−b ±(√(b^2 −4ac)))) as the quadratic formula? i proved it.


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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

$okay sirs thank you, was just wondering why$ $this formula is so negleted$
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