Results and Formulas of Equations

If and are the roots of the Quadratic Equation , then

The sum and products of the roots and of are given by and

is called the discriminant of

The roots of the quadratic are


imaginary if is negative.

real if is positive or zero.

real and equal if .

real and rational if and is a perfect square or zero.

real and irrational if and is not a perfect square.


The equation whose roots are and (given) is given by

, and where and are called the cube root of unity.

and are called the complex cube root of unity.

Each of the complex cube roots of unity are the square of the other.

The sum of the cube roots of unity is zero. i.e.,


If , and are the roots of then

If ,, and are the roots of then