The Quadratic Formula

How to use the Quadratic Formula to solve quadratic equations

ax

^{2}+ bx + c = 0- a, b are coefficients

{−b ± √(b

^{2}− 4ac)} ÷ 2a- Discriminant = b
^{2}− 4ac- Discriminant >0, Two real solutions
- Discriminant = 0, One real solution
- Discriminant < 1, No real solutions
- Complex solutions

Next target: Complex numbers

The Distributive property

Formulae/equations, changing the subject

__Derivation:__ax

^{2}+ bx + c = 0a(x

^{2}+^{b}/_{a}+^{c}/_{a}) = 0x

^{2}+^{b}/_{a}+^{c}/_{a}= 0Completing the square:

(x +

^{b}/_{2a})^{2}− b^{2}/4a^{2}+^{c}/_{a}= 0Solve for x:

(x +

^{b}/_{2a})^{2}= b^{2}/4a^{2}−^{c}/_{a}x + b/2a = ±√(b

^{2}/4a^{2}−^{c}/_{a})x = −b/2a ± √(b

^{2}− 4a^{2}c/a) ÷ 2a