Question

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 1

A

Explanation:

We can find the roots of this function by factoring the trinomial and setting each factor equal to 0 to solve for x.

Trinomials are three term algebraic expressions typically featuring variables to exponent powers. To break these trinomials down we factor them using the diamond method or GCF. The diamond method states that for a trinomial
`ax^2+bx+c` multiply a*c then find two numbers which multiply to this number and add to b. When you find those numbers, write them as
`(x-/+ number)(x-/+number)`.

`x^2-8x+12`

a=1, c=12

ac=12 and add to b=-8 which are -2 and -6

So (x-2)(x-6) are the factors. We set each equal to 0 and solve for x.

(x-2)=0

x=2

(x-6)=0

x=6

{2,6} are the roots of the function.