Question

AYUDAAA URGE :C Ecuaciones cuadráticas por formula general porfa. 1.- x^2-2x-3=0 2.- 6x^2+7x=3 3.- 3x^2+6x-2=0 Primero sacar valor discriminante porfa
50 PUNTOS

Answer 1

Si:
ax² + bx + c = 0

Entonces:
Discriminante: D = b² - 4*a*c

Raíces:
$x_{1} =\frac{-b+ \sqrt{D} }{2a}$
$x_{2} =\frac{-b- \sqrt{D} }{2a}$

1.
x²-2x-3=0

D = (-2)² - 4*1*(-3)
D = 4 + 12
D = 16

Raíces:
$x_{1} =\frac{-(-2)+ \sqrt{16} }{2*1}$
$x_{1} =\frac{2+ 4 }{2}$
$x_{1} =\frac{6}{2}$
$x_{1} =3$

$x_{2} =\frac{-(-2)- \sqrt{16} }{2*1}$
$x_{2} =\frac{2- 4 }{2}$
$x_{2} =\frac{-2}{2}$
$x_{2} =-1$

2.
6x² + 7x = 3
6x² + 7x - 3 = 0

D = (7)² - 4*6*(-3)
D = 49 + 72
D = 121

Raíces:
$x_{1} =\frac{-(7)+ \sqrt{121} }{2*6}$
$x_{1} =\frac{-7+ 11 }{12}$
$x_{1} =\frac{4}{12}$
$x_{1} =1/3$

$x_{2} =\frac{-(7)- \sqrt{121} }{2*6}$
$x_{2} =\frac{-7- 11 }{12}$
$x_{2} =\frac{-18}{12}$
$x_{2} =-3/2$

3.
3x² + 6x - 2 = 0

D = (6)² - 4*3*(-2)
D = 36 + 24
D = 60

Raíces:
$x_{1} =\frac{-(6)+ \sqrt{60} }{2*3}$
$x_{1} =\frac{-6+ 2\sqrt{15}}{6}$
$x_{1} =\frac{-3+ \sqrt{15}}{3}$

$x_{2} =\frac{-(6)- \sqrt{60} }{2*3}$
$x_{2} =\frac{-6- 2\sqrt{15}}{6}$
$x_{2} =\frac{-3- \sqrt{15}}{3}$

Saludos.

Answer 2

x²-2x-3=0
x²-3x+x-3=0
x(x-3) + (x-3)=0

(x-3).x=0

x=0  o   x=3


- 6x^2+7x+3=0

x= -7+-√49-4(-6)(3) / 2(-6)
x= 1/3  o  x= -2/3



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