Recordem: Equacions 2n grau incompletes

5. Equació 2n grau

5.1. Equacions 2n grau incompletes

Una equació de 2n grau $a x squared plus b x plus c equals 0$ és incompleta quan els coeficient b o c són zero

- Cas $b equals 0$

$bold italic a bold italic x to the power of bold 2 bold plus bold italic c bold equals bold 0$

$a x squared equals negative c space space space rightwards arrow space space x squared equals negative c over a space space space space rightwards arrow space space space space x equals bold plus-or-minus square root of bold minus bold c over bold a end root$

Exemples

$4 x squared minus 25 equals 0 space space space rightwards arrow space space space space space 4 x squared equals 25 space space rightwards arrow space space x squared equals 25 over 4 space space space rightwards arrow space space x equals plus-or-minus square root of 25 over 4 end root equals plus-or-minus 5 over 2$

$4 x squared plus 25 equals 0 space space space rightwards arrow space space space space space 4 x squared equals negative 25 space space rightwards arrow space space x squared equals negative 25 over 4 space space space rightwards arrow space space x equals plus-or-minus square root of negative 25 over 4 end root space space space N o space t é space s o l u c i ó$

- Cas $c equals 0$

$bold italic a bold italic x to the power of bold 2 bold plus bold italic b bold italic x bold equals bold 0$

$x left parenthesis a x plus b right parenthesis equals 0 space space rightwards arrow space space open curly brackets table attributes columnalign left end attributes row cell bold italic x bold equals bold 0 end cell row cell a x plus b equals 0 space space rightwards arrow space a x equals negative b space space rightwards arrow space space bold italic x bold equals bold minus bold b over bold a end cell end table close$

Exemples

$3 x squared plus 5 x equals 0 space space space rightwards arrow space space x left parenthesis 3 x plus 5 right parenthesis equals 0 space space space rightwards arrow space open curly brackets table attributes columnalign left end attributes row cell x equals bold 0 end cell row cell 3 x plus 5 equals 0 space space rightwards arrow 3 x equals negative 5 space space rightwards arrow space x equals bold minus bold 5 over bold 3 end cell end table close$

$x squared minus 5 x equals 0 space space space rightwards arrow space space x left parenthesis x minus 5 right parenthesis equals 0 space space space rightwards arrow space open curly brackets table attributes columnalign left end attributes row cell x equals bold 0 end cell row cell x minus 5 equals 0 space space rightwards arrow x equals bold 5 end cell end table close$

Propietat intel·lectual i drets d'autoria

5. Equació 2n grau

5.1. Equacions 2n grau incompletes