Algebra

Factorization of Quadratic Equation

The solution of a quadratic equation   ax² + bx + c = 0   is given by:

x

=

–b ± √ b2 – 4ac 2a

This is derived as follows: We have

ax2 + bx + c

=

0

dividing through by a:

x2 +

b a

x +

c a

=

0

 factorizing:

x  +

b 2a

2

–

b2 4a2

+

c a

=

0

 so

x  +

b 2a

2

=

b2 – 4ac 4a2

taking square roots of both sides

x  +

b 2a

=

±√ b2 – 4ac 2a

and hence the result.