Question

Utilizando la Fórmula General resuelve las siguientes ecuaciones.

a) x2 + 2x – 8 = 0

b) 8x2 – 2x – 3 = 0

c) 2x2 + 9x + 10 = 0

Answer 1

Explicación paso a paso:

a) x2 + 2x – 8 = 0

$x = \frac{ -b \frac{ + }{ - } \sqrt{ {b}^{2} - 4ac } }{2a} = \frac{ -2 \frac{ + }{ - } \sqrt{ {(2)}^{2} - 4(1)( - 8) } }{2(1)} = \frac{ -2 \frac{ + }{ - } \sqrt{ 4 + 32 } }{2} = \frac{ -2 \frac{ + }{ - } \sqrt{ 36 } }{2} = \frac{ -2 \frac{ + }{ - } 6 }{2} = \\ x1 = \frac{4}{2} = 2 \\ x2 = \frac{ - 8}{2} = - 4$

b) 8x2 – 2x – 3 = 0

$x = \frac{ -b \frac{ + }{ - } \sqrt{ {b}^{2} - 4ac } }{2a} = \frac{ - ( -2 )\frac{ + }{ - } \sqrt{ {( - 2)}^{2} - 4(8)( - 3) } }{2(8)} = \frac{ 2 \frac{ + }{ - } \sqrt{ 4 + 96 } }{16} = \frac{ 2 \frac{ + }{ - } \sqrt{ 100 } }{16} = \frac{ 2 \frac{ + }{ - } 10 }{16} = \\ x1 = \frac{12}{16} = \frac{3}{4} \\ x2 = \frac{ - 8}{16} = - \frac{1}{2}$

c) 2x2 + 9x + 10 = 0

$x = \frac{ -b \frac{ + }{ - } \sqrt{ {b}^{2} - 4ac } }{2a} = \frac{ -9 \frac{ + }{ - } \sqrt{ {(9)}^{2} - 4(2)( 10) } }{2(2)} = \frac{ -9 \frac{ + }{ - } \sqrt{ 81 - 80 } }{4} = \frac{ -9 \frac{ + }{ - } \sqrt{ 1 } }{4} = \frac{ -9\frac{ + }{ - } 1 }{4} = \\ x1 = \frac{ - 8}{4} = - 2 \\ x2 = \frac{ - 10}{4} = - \frac{5}{2}$