Quadratic Equation
Quadratic equation is in the form
 

Where
a, b, & c = real-number constants
a & b = numerical coefficient or simply coefficients
a = coefficient of x²
b = coefficient of x
c = constant term or simply constant
a cannot be equal to zero while either b or c can be zero
 

Examples of Quadratic Equation
Some quadratic equation may not look like the one above. The general appearance of quadratic equation is a second degree curve so that the degree power of one variable is twice of another variable. Below are examples of equations that can be considered as quadratic.

1.

2.

3.

4.

5.

6.

7.
 

For us to see that the above examples can be treated as quadratic equation, we take example no. 6 above, 10x^1/3 + x^1/6 - 2 = 0. Let x^1/6 = z, thus, x^1/3 = z². The equation can now be written in the form 10z² + z - 2 = 0, which shows clearly to be quadratic equation.
 

Roots of a Quadratic Equation
The equation ax² + bx + c = 0 can be factored into the form
 

Where x₁ and x₂ are the roots of ax² + bx + c = 0.
 

Quadratic Formula
For the quadratic equation ax² + bx + c = 0,
 

See the derivation of quadratic formula here.
 

The quantity b² - 4ac inside the radical is called discriminat.
•   If b² - 4ac = 0, the roots are real and equal.
•   If b² - 4ac > 0, the roots are real and unequal.
•   If b² - 4ac  

Sum and Product of Roots
If the roots of the quadratic equation ax² + bx + c = 0 are x₁ and x₂, then
 

Sum of roots

Product of roots

You may see the derivation of formulas for sum and product of roots here.