What are the roots of this function? f(x) = x2 – 8x + 12 A) {2, 6} B) {8, 12} C) {-3, -4} D) {-4, -4}

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) = 0By zero product property ; we have⇒x -6 = 0 and x -2 = 0⇒x =6 and x = 2Therefore, the roots of the function  [tex]f(x) = x^2-8x +12[/tex] is, 2 and 6