Sum and product of roots of quadratic equation

From the given equation: a = 1, b = -2, and c = 5
 

Sum of roots
$x_1 + x_2 = -\dfrac{b}{a}$

$x_1 + x_2 = -\dfrac{-2}{1}$

$x_1 + x_2 = 2$           answer
 

Product of roots
$x_1 x_2 = \dfrac{c}{a}$

$x_1 x_2 = \dfrac{5}{1}$

$x_1 x_2 = 5$   ←   answer

From the given equation: a = 1, b = -2, and c = 5
 

Using the quadratic formula
$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$x = \dfrac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(5)}}{2(1)}$

$x = \dfrac{2 \pm \sqrt{-16}}{2}$

$x = \dfrac{2 \pm 4i}{2}$

$x = (1 + 2i) \, \text{ and } \, (1 - 2i)$   ←   roots of the given equation
 

$x_1 = 1 + 2i$

$x_2 = 1 - 2i$
 

Sum of roots
$x_1 + x_2 = (1 + 2i) + (1 - 2i)$

$x_1 + x_2 = 2$   ←   answer
 

Product of roots
$x_1 x_2 = (1 + 2i)(1 - 2i)$

$x_1 x_2 = 1 - 4i^2$

$x_1 x_2 = 1 - 4(-1)$

$x_1 x_2 = 5$   ←   answer