Step-by-step explanation:
the x-intercepts are the points, where y=0.
x² - 6x + 5 = 0
with experience I see right away, this is true for x=1 and x=5.
but let's solve this formally.
the general solution to a quadratic excision is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = -6
c = 5
x = (6 ± sqrt((-6)² - 4×1×5))/2 = (6 ± sqrt(36-20))/2 =
= (6 ± sqrt(16))/2 = (6 ± 4)/2 = 3 ± 2
x1 = 3+2 = 5
x2 = 3-2 = 1
so, the 2 x-intercept points are
(1, 0) and (5, 0)
