Arithmetic Course/Polynominal Equation

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Polynominal Equation[edit]

An equation is an expression of one variable such that

Solving Polynominal Equation[edit]

Solving polynominal equations involves finding all the values of variable x that satisfy f(x) = 0.

First Order Equation[edit]

A first order polynominal equation of one variable x has the general form

Ax + B = 0

Rewrite the equation above

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle x = -\frac{B}{A}}

Second Order Equation[edit]

A second order polynominal equation of one variable x has the general form

  1. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle Ax^2 + Bx + C = 0}

Solving Equation[edit]

Method 1[edit]

Where


Depending on the value of the equation will have the following root

One Real Root

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle -\alpha = - \frac{B}{2A}}

Two Real Roots

Two Complex Roots

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle -\alpha \pm j\lambda }

Method 2[edit]

Method 3[edit]