Basics

#math/notes

Quadratic Equation

x=−b±b2−4ac2a

Finding the terms without a calculator

Since,

(x−a)(x−b)=x2+x(a+b)+ab

To find a and b, need to find where

a+b=ab

So,

  1. find factors of the last term (ab)
  2. Check if those 2 factors can be added together to give (a+b)
Example

x2+7x+12
Factors of 12

Factor (a) Factor (b) Add result (a+b)
1 12 13
2 6 8
3 4 7
Since 3+4==7 which is the middle term (7x),
a=3,b=4