Matematica Semana 2
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MATEMÁTICA
Ecuación de 2do Grado
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Ecuaciones de segundo grado
Son del tipo:
002 acbxax1) Ecuaciones incompletas (b=0 ó c=o)
1.1) b=0 EJEMPLO: 082 2 x
Se resuelve como si fuese de primer grado
4
82
2
2
x
x 21 x
22 x
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1) Ecuaciones incompletas (b=0 ó c=o)
1.2) c=0
EJEMPLO:
082 2 xx Se saca factor común a x
082 xx
0x 082 x
4x
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2) Ecuaciones completas:
EJEMPLO:
0352 2 xx
Se aplica la fórmula
a
cabbx
2
42
2a
3c
5b
2.2
)3.(2.455 2 x
4
24255 x
4
75x
4
75x
4
75x
4
2x
4
12x
2
1x
3x
0,, cba
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Se llama DISCRIMINANTE de una ecuación de segundo grado al valor:
cab 42
El nº de soluciones de una ecuación de segundo
grado dependerá del SIGNO del Determinante
Si:
> 0 Tiene 2 soluciones reales distintas
= 0 Tiene 1 solución DOBLE
< 0 No tiene solución
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Demostración de la fórmula de la ecuación de segundo grado
02 cbxax Se multiplican los dos miembros por 4a
0444 22 acabxxa Se suma y resta b2
0444 2222 acbbabxxa Se completan cuadrados
04)2( 22 acbbax
acbbax 42 22
acbbax 42 2
a
acbbx
2
42 Se despeja x
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Propiedades de las raíces de una
ecuación de segundo grado
1) Suma de raíces a
bxx
21
A partir de la fórmula se obtienen las siguientes propiedades
2) Producto de raíces a
cxx 21
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0322 xx
Resolver
042 x
0784 2 xx
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EJERCICIOS
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