Math Formulas: Solutions of algebraic equations

Quadric Equation: ax² + bx + c = 0

Solutions (roots):

If D = b² - 4ac is the discriminant , then the roots are

1) real and unique if D > 0

2) real and equal if D = 0

3) complex conjugate if D < 0

Cubic Equation: x³+ a₁x² + a₂x + a₃ = 0

Let

Then solutions (roots) are:

If D = Q³ + R³ is the discriminant , then:

1) one root is real and two complex conjugate if D > 0

2) all roots are real and at last two are equal if D = 0

3) all roots are real and unequal if D < 0

Quartic Equation: x⁴+ a₁x³ + a₂x² + a₃x + a₄ = 0

Let y₁ be a real root of the cubic equation

Solutions are the 4 roots of