# Algebraic Formulas

## Arithmetic mean, Geometric mean, Powers and Exponents, The Equation I and II degree

### Weighted arithmetic mean:

,

where a1, a2, ..., an represent numbers with weights p1, p2, ..., pn.

### Powers:

### First degree equations:

A first degree equation has the form: ax+b=0.

The solution for this equation is x = -b/a, with a different  0.

If a = 0 and b different 0, the solution is void (empty set). Thus, i.e. if a = 0 and b = 0, the solution is the whole lot of definition.

### Ecuatia de gradul al II-lea:

The canonical form of an equation second degree is: ax2+bx+c=0. The steps to solve this type of equation are:

•  Calculate the discriminant:
• Evaluate the discriminant (Δ):
• if the discrimnant is negative (Δ < 0), the equation has no solutions in real's set;
• if the discrimnant is nul (Δ = 0), the equation has only one solution in the real's set (x1 = x2);
• if the discrimnant is positive (Δ > 0), the equation has only two solutions;
• Calculate the solutions:

### Relations between the roots of second degree equation

Keywords: formulas algebra, arithmetic mean, geometric mean calculation formulas Powers abbreviated equation degree Ec. gr. II. Relations between the roots of the equation grade II