Explicación paso a paso:
1) x²-2x-3=0
x -3
x 1
(x-3) (x+1 ) =0
i)x - 3 = 0
x = 3
ii)x +1 =0
x = -1
Por tanto, x es 3 y -1
2) -x²-x = 0
Hallaremos x con la formula genral:
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Dato:
a = -1
b = -1
[tex]x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\left(-1\right)\cdot \:0}}{2\left(-1\right)}\\\\x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left1-0}}{2\left(-1\right)}\\\\x_{1,\:2}=\frac{-\left(-1\right)\pm \:1}{2\left(-1\right)}\\\\x_1=\frac{-\left(-1\right)+1}{2\left(-1\right)},\:x_2=\frac{-\left(-1\right)-1}{2\left(-1\right)}\\\\x_1 = \frac{1+1}{-2} ,\: x_2 = \frac{1-1}{-2} \\\\x_1 = \frac{2}{-2} ,\: x_2 = \frac{0}{-2} \\\\x_1 = -1 ,\: x_2 = 0 \\[/tex]
