Respuesta:
Explicación paso a paso:
a) 2x² + 3x - 9 = 0
2x - 3
x + 3
(2x - 3)(x + 3) = 0
2x - 3 = 0 => [tex]x_{1}[/tex] = 3/2
x + 3 = 0 => [tex]x_{2}[/tex] = - 3
b) ax² + bx + c = 0
Discriminante D
D = b² - 4ac
22x² + 7x - 30 = 0
a = 22 ; b = 7 ; c = -30
D = 7² - 4(22)(-30) = 2868 >0
Existen dos raíces reales diferentes
Fórmula general
[tex]x = \frac{-b\± \sqrt{b^{2}-4ac } }{2a}[/tex]
[tex]x = \frac{-7\± \sqrt{2869 }}{2(22)} = \frac{-7\± \sqrt{2869 }}{44}[/tex]
[tex]x_{1} =\frac{-7+ \sqrt{2869 }}{44}[/tex]
[tex]x_{2} =\frac{-7- \sqrt{2869 }}{44}[/tex]
c) 12x² - 2x - 4 = 0
entre 2 a toda la ecuación
6x² - x - 2 = 0
3x - 2
2x + 1
(3x - 2)(2x + 1) = 0
3x - 2 = 0 => [tex]x_{1}[/tex] = 2/3
2 x + 1 = 0 => [tex]x_{2}[/tex] = - 1/2
d) x² + 2x - 15 = 0
(x - 3)(x + 5) = 0
x - 3 = 0 => [tex]x_{1}[/tex] = 3
x + 5 = 0 => [tex]x_{2}[/tex] = - 5
e) 8x² + 12x = 0
4x(2x + 3) = 0
x = 0 => [tex]x_{1}[/tex] = 0
2x + 3 = 0 => [tex]x_{2}[/tex] = - 3/2
