Answer:
Option A is correct.
the root of the given function is, {2, 6}
Step-by-step explanation:
Given the function: [tex]f(x) = x^2-8x +12[/tex]
To find the root of the given function;
Set f(x) = 0
⇒[tex]x^2-8x+12 =0[/tex]
In the Quadratic Factorization using Splitting of Middle Term which is x term is the sum of two factors and product equal to last term.
Step 1. Find the product of 1st term and the last.
Product = [tex]1 \times 12 =12[/tex]
Step 2. Find the factors of 12 in such way that addition or subtraction of that factors is the middle term, i.e -8x(Splitting of middle term)
Factor = [tex]-6 \text{and} -2[/tex]
Therefore, -6-2= -8
Step 3. Group the terms to form pairs:
[tex]x^2-6x-2x+12 =0[/tex]
[tex]x(x-6)-2(x-6) =0[/tex]
(x-6)(x-2) = 0
By zero product property ; we have
⇒x -6 = 0 and x -2 = 0
⇒x =6 and x = 2
Therefore, the roots of the function [tex]f(x) = x^2-8x +12[/tex] is, 2 and 6
