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Ivahew [28]
3 years ago
11

Descried how to derive the quadratic formula from a quadratic equation in standard form

Mathematics
1 answer:
Aleks [24]3 years ago
8 0

Answer:

The standard form of a quadratic equation is:

ax^2+bx+c=0, a\neq 0

Quadratic Formula Derivation:

ax^2+bx+c=0\\

$x^2+\frac{b}{a}x+\frac{c}{a} =0 $

$x^2+\frac{b}{a}x = -\frac{c}{a}$

Completing the Square:

$x^2+\frac{b}{a}x +\frac{b^2}{4a^2} = \frac{b^2}{4a^2}-\frac{c}{a}$

$  ( x+\frac{b}{2a} )^2 =  \frac{b^2-4ac}{4a^2}  $

Square Root property:

$x+\frac{b}{2a}  = \pm \sqrt{ \frac{b^2-4ac}{4a^2}}   $

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

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

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