# Algebraic Formulas

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

### Arithmetic mean (average):

### Geometric mean (proportional):

### Weighted arithmetic mean:

,

where **a**_{1}, a_{2}, ..., a_{n} represent numbers with weights **p**_{1}, p_{2}, ..., p_{n}.

### Powers:

### Formulas for calculating short

### First degree equations:

A first degree equation has the form: **a***x*+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: **a***x*^{2}+b*x*+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 (x
_{1} = x_{2});
- 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

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