Question

Resuelve las siguientes ecuaciones usando la fórmula general para resolver ecuaciones cuadráticas
A: x2 + 3X - 10= 0
B: x2 - 3x - 4 = 0
C: -x2 - 4x - 2 = 0
D: -2 x2 - x = -6
e: (x+2)2 + 1= 0
f: (x - 3)2 - 4 = 0
g: -0.5 x2 + 2x + 1.5 = 0
h: 1.5 x2 + 2x = 0

Answer 1

Respuesta:

A ) 3±√ 3^2 - 4 ( 1 )( - 10 ) / 2 ( 1 )

3 ± √ 9 + 40 / 2

3 ± √49 / 2

3 ± 7 / 2

10 / 2 = 5

x1 = 5

x2 = 3 - 7 / 2

x2 = - 4 / 2

x2 = - 2

b ) x ^2 - 3x - 4 = 0

- 3 ± √- 3^2 - 4 ( 1 )( - 4 ) / 2 ( 1 )

- 3 ± √- 9 + 16 / 2

- 3 ± 7 / 2

4 / 2 = 2

x1 = 2

- 3 - 7 / 2

- 10 / 2 = - 5

x2 = - 5

c ) - x^2 - 4x - 2 = 0

- 4 ± √- 4 ^2 - 4 ( - 1 )( - 2 ) / 2 ( - 1 )

- 4 ± √- 16 - 8 / - 2

- 4 ± √-24 / - 2

- 4 ± - 24 / - 2

- 28 / - 2

x1 = 14

- 4 - ( - 24 ) = 20 / - 2

x2 = - 10

d ) - 2 * x^2 - x = - 6

- 2x^2 - x = - 6

- 1 ± √ -1^2 - 4 ( - 2 ) ( 6 ) / 2 ( - 2 )

- 1 ± √- 49 / - 4

- 1 + - 49 / - 4

- 50 / - 4

x1 = 12.5

- 1 - ( - 50 ) / - 4

49 / - 4

x2 = - 12.25

e ) x^2 - 2.3x + 9 - 4 = 0

x^2 - 6x + 5 = 0

- 6 ± √- 6^2 - 4 ( 1 ) ( 5 ) / 2 ( 1 )

- 6 ± √ - 56 / 2

- 6 ± - 56 / 2

- 62 / 2

x1 = - 31

- 6 - ( - 56 ) / 2

- 6 + 50 / 2

x2 = 25

g ) - 0.5x^2 + 2x + 1.5 = 0

2 ± √ 2^2 - 4 ( - 0.5 )( 1.5 ) / 2 (- 0.5 )

2 ± √ 4 - 3 /  - 1

2 ± 1 / - 1

3 / - 1

x1 = - 3

2 - 1 / - 1

x2 = 1 / - 1

x2 = - 1

h ) 1.5x^2 + 2x = 0

2± √2^2 - 4 ( 1.5 ) / 2 ( 1.5 )

2 ± √4 - 2 / 3

2 ± 1.41421 / 3

3.41421 / 3

x1 = 1.13807

2 - 1.41421 / 3

0.58579 / 3

x2 = 0.19526

Explicación paso a paso: