Math formulas: Solutions of algebraic equations

0 formulas included in custom cheat sheet

Quadric Equation:

Solutions (roots):

If is the discriminant , then the roots are

1. real and unique if

2. real and equal if

3. complex conjugate if

Cubic Equation:

Let

Then solutions (roots) of the cubic equation are:

If is the discriminant of the cubic equation, then:

1. one root is real and two complex conjugate if

2. all roots are real and at last two are equal if

3. all roots are real and unequal if

Quartic Equation:

Let be a real root of the cubic equation

Then solutions of the quartic equation are the 4 roots of