Answer:
x = 2 or x = 6
Step-by-step explanation:
We have the equation: x² - 8x + 12 = 0,
The general factored for for a quadratic equation is (x - h)( x - k) = 0, were h and k are the roots.
To write the equation in this form, we have to find α (-h) and β (-k) in which
α * β = 12
and
α + β = - 8
Some possibilities to α * β = 12 are 3*4, (-3)*(-4), 2*6 and (-2)*(-6)
From this possibilities, the only alternative that results in α + β = - 8 is (-2) and (-6).
Now, we can write the equation in the quadratic form:
(x - 2)( x - 6) = 0.
To solve find the roots:
(x - 2) = 0
x = 2
or
(x - 6) = 0
x = 6
