Quadratic Formula

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Last modified by

on

Jul 24, 2020, 6:28:07 PM

Created by

on

Dec 6, 2013, 4:38:18 PM

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

$"Quadratic Solutions" = (- "b" +- sqrt( "b" ^2 -4* "a" * "c" ))/(2* "a" )$

a

b

c

Notes

Solving the quadratic equation.
Suppose $a x^2+b x+c=0$ and $a!=0$

first divide by $a$ to get:

$x^2+b/a x+c/a=0$

Then complete the square and obtain:

$x^2+b/a x+(b/(2a))^2-(b/(2a))^2+c/a=0$

The first three terms factor:

$(x+b/(2a))^2=(b^2)/(4a^2)-c/a$

Take square roots on both sides to get

$x+b/(2a)=+-sqrt((b^2)/(4a^2)-c/a)$

Finally move the b/(2a) to the right and simplify to get the two solutions:

$x_(1,2)=(-b+-sqrt(b^2-4a c))/(2a)$

This equation, Quadratic Formula, is used in 1 page

• Algebra Calc by Wilfried

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