Results and Formulas of Equations

If and are the roots of the Quadratic Equation , then

Sum and products of the roots and of is given by and

is called 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 cube root of unity.

and are called the complex cube root of unity.

Each of the complex cube roots of unity is 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