Question

What are the zeros of the function f(x) = f of x equals three x squared minus nine x plus six divided by quantity three x minus three ?
@jim_thompson5910

Answer 1

\[\Large f(x) = \frac{3x^2 - 9x+6}{3x-3}\]

right?

Answer 2

yes

Answer 3

plug in f(x) = 0 and solve for x

Answer 4

thats it ?

Answer 5

\[\Large f(x) = \frac{3x^2 - 9x+6}{3x-3}\]

\[\Large 0 = \frac{3x^2 - 9x+6}{3x-3}\]

\[\Large 0(3x-3) = 3x^2 - 9x+6\]

\[\Large 0 = 3x^2 - 9x+6\]

\[\Large 3x^2 - 9x+6 = 0\]

\[\Large 3(x^2 - 3x+2) = 0\]

\[\Large 3(x-2)(x-1) = 0\]

I'll let you finish up

Answer 6

is it 2?

Answer 7

that's one solution

there's one more

Answer 8

3(x-2)(x-1) = 0

turns into

x-2 = 0 or x-1 = 0

x = 2 or x = ???

Answer 9

1

Answer 10

correct

x = 2, x = 1

are your two roots/zeros

Answer 11

ok so for my homework they have both 1 and 2 which would be my answer ?

Answer 12

yes, both are part of the solution set

Answer 13

but i can only pick one answer

Answer 14

hmm odd, there's no "select all that apply" ?

Answer 15

no theres -1, 1, 2, and -2

Answer 16

oh I'm not thinking lol

Answer 17

in the denominator, we have 3x-3

if x = 1, then 3x-3 = 3*1-3 = 3-3 = 0

you cannot divide by zero, so x = 1 is NOT in the domain

Answer 18

only x = 2 is the solution

Answer 19

oh ok thank you next question !