Más contenido relacionado Similar a INECUACIONES CUADRATICAS.pptx (20) INECUACIONES CUADRATICAS.pptx2. EJERCICIOS
Resolver la desigualdad indicada, dar la solución
en términos de intervalos.
1. 2x2 – 10x – 6 < x2– 5x + 8
2. x2 + 7x +5 < 12x + 1
3. x2 + 3x – 4 > 0
3. EJERCICIOS
Resolver la desigualdad indicada, dar la solución en términos de
intervalos.
1. 2x2 – 10x – 6 < x2– 5x + 8
2x2 – 10x – 6 < x2 – 5x + 8
2x2 – 10x – 6 – x2 + 5x – 8 < 0
x2 – 5x – 14 < 0 factorizar: x2 – 5x – 14 = (x – 7 ) (x + 2 ) = 0
(x – 7) (x + 2) < 0 x – 7 = 0 x = 7 x + 2 = 0 x = – 2
X < – 2 – 2 < x < 7 X > 7
X= – 4 X= 0 X= 10
-∞ +∞
(-∞,-2) (-2,7) (7,+∞)
(x-7) -4-7 = -11 =- 0-7 = -7 = - 10 -7 = 3 = +
(x+2) -4+2 = -2 = - 0+2 = 2 = + 10 +2 = 12 = +
x2 – 5x – 14 + 22 = + (F) - 14 = - (V) 36 = + (F)
Resultado: – 2 < X < 7 = (-2,7)
4. EJERCICIOS
Resolver la desigualdad indicada, dar la solución en
términos de intervalos.
1. x2 – 5x – 14 < 0 factorizar: x2 – 5x – 14 = 0
(x – 7) (x + 2) < 0 a=1 b=-5 c=-14
x = {-b +/- raiz (b2 – 4.a.c )} / (2.a)
x={-(-5)+/- raiz ((-5)2 – 4.1.-14 )} / (2.1)
x={5+/-raiz (25 +56 )} / (2)= {5+/-raiz (81)} / (2)=(5 +/- 9)/2
x=(5+9)/2 =14/2=7 y x=(5-9)/2 =-4/2=-2
(-∞,-2) (-2,7) (7,+∞)
(x-7) -4-7 = -11 =- 0-7 = -7 = - 10 -7 = 3 = +
(x+2) -4+2 = -2 = - 0+2 = 2 = + 10 +2 = 12 = +
x2 – 5x – 14 + 22 = + (F) - 14 = - (V) 36 = + (F)
Resultado: – 2 < X < 7 = (-2,7)
5. EJERCICIOS
Resolver la desigualdad indicada, dar la solución en términos de
intervalos.
2. x2 + 7x +5 < 12x + 1
x2 + 7x +5 < 12x + 1
X2 + 7x +5 – 12x – 1 < 0
x2 – 5x + 4 < 0 factorizar: x2 – 5x + 4 = (x – 4 ) (x – 1 ) = 0
(x – 4) (x – 1) < 0 x – 4 = 0 x = 4 x – 1 = 0 x = 1
X < 1 1 < x < 4 X > 4
X= 0 X= 2 X= 5
-∞ +∞
(-∞,1) (1,4) (4,+∞)
(x–4) 0 – 4 = – 4 = – 2 – 4 = – 2 = – 5 – 4 = 1 = +
(x–1) 0 – 1 = – 1 = – 2 – 1 = 1 = + 5 – 1 = 4 = +
x2 – 5x + 4 + 4 = + (F) – 2 = – (V) 4 = + (F)
Resultado: 1 < X < 4 = (1,4)
6. EJERCICIOS
Resolver la desigualdad indicada, dar la solución en
términos de intervalos.
3. x2 + 3x – 4 > 0
x2 + 3x – 4 > 0 factorizar:x2 + 3x – 4 = 0;(x + 4 ) (x – 1 ) =0
(x + 4) (x – 1) > 0 x + 4 = 0 x = – 4 x – 1 = 0 x = 1
X < – 4 – 4 < x < 1 X > 1
X= - 5 X= 0 X= 2
-∞ +∞
(-∞, –4) (–4,1) (1,+∞)
(x+4) –5+4= – 1 = – 0 + 4 = 4 = + 2 + 4 = 6 = +
(x–1) –5–1 = –6 = – 0 – 1 = –1 = – 2 – 1 = 1 = +
x2 – 5x + 4 +6 = + (V) – 4 = – (F) 6 = + (V)
Resultado: (-∞, –4) U (1,+∞)