Roots of equations

Roots of equations

Is y=f(x). The values of x that make  y= 0 are called roots of the equation. The fundamental theorem of algebra states that every polynomial of degree n has n roots. In the caseof real estate, it must correspond to x values that make the feature cut the x-axis:

The roots of a polynomial can be real or complex. If a polynomial has coefficients a0, a1, a2,…an-1, an, real,then all the complex roots always occur in complex conjugate pairs. For example, a cubic polynomial has the following general form:

f(x)= a0x3+ a1x2+ a2x+ a3

The fundamental theorem of algebrastates that a polynomial of degree n has n roots. In the case of cubic polynomial can be the following:

·         Three distinct real roots.

·         A real root with multiplicity 3.·         A simple real root and one real root with multiplicity 2.

·         One real root and a complex conjugate pair.

Example. The roots of these polynomials are summarized below.1.       Three distinct real roots:

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For their study, the functions can beclassified into algebraic and transcendental.

Algebraic functions

Let g = f (x) the function expressed

fnyn+ fn-1yn-1+…+ f1y+ f0=0

Where fi is a polynomial of order i in x.   Polynomials area simple case of algebraic functions that are usually represented as

fn(x)=a0+a1x+ a2x2…+ anxn

Where n is the order of the polynomial.

Example.

f2(x) = 1-2.37 x + 7.5 x 2f6(x) = 5 x 2-x 3 + 7 x 6

Transcendental functions

Are those that are not algebraic. They include the trigonometric, exponential, logarithmic, among others.

Example.

f(x) = lnx2-1f(x) = e-0.2xsin(3x-5) 

The methods described in this unit require that the function is differentiable in the range where they apply. If the methods used in non-differentiable or discontinuous functions at some...