given function f(x)=x2-6x+8, find x, if f(x)=0?

(x-4)(x-2) = 0

so x = 4 or 2

f(x) = 0

plug 0 for f(x)

0 = x^2 – 6x + 8

factor

look for two numbers that multiply to 8 and add to -6

the two numbers are -2 and -4

since the leading coefficient is 1, plug in the two numbers in factor form (x + a) (x + b)

(x – 2) (x – 4) = 0

set each quanity equal to 0

x – 2 = 0

x = 2

x – 4 = 0

x = 4

so x = 2 or 4