Question

Give the x-intercepts of the graph of the equation below.
I just need to check my answer

Answer 1

\[f(x)= \frac{ x ^{2}-5x+4 }{ x ^{2}+5x+6 }\]

Answer 2

Is it (2,3)?

Answer 3

@welshfella

Answer 4

give me a moment i have to go for a few minutes

Answer 5

okay

Answer 6

right

well you just equate f(x) to zero and solve for x

x^2 - 5x + 4 = 0

Answer 7

the denominator can be ignored
because 5x^2 - 5x + 4 = 0 * (x^2 + 5x + 6)

Answer 8

x^2 - 5x + 4 can be factored

Answer 9

(2,3) is not correct

Answer 10

@phi

Answer 11

@mustafa2014 can you please help me

Answer 12

do you know how to factor the "top"
x^2 -5x + 4 ?

Answer 13

i think so yes

Answer 14

list all the pairs of ways to get 4:
1,4
2,2

the + sign on the 4 means the factors will have the same sign
the - sign on the -5 means the largest factor is -. that means both factors are -

now make both numbers in the pairs negative and add them
-1 + -4 = -5
-2 + -2 = -4

if you get a pair that add up to the -5 (from -5x term)
those are the factors

Answer 15

so they're -1, 4

Answer 16

so you the factors will be
(x-1)(x-4)
if we multiply that out using FOIL for example, you get x^2 -5x +4
so that looks good

Answer 17

yes
so the next step would be to factor the bottom?

Answer 18

the question asks for the "zeros"
the fraction will be zero if the top is zero (and the bottom isn't)
all we really want are the ways for the top to be zero.

Answer 19

we want
(x-1)(x-4) = 0
you can think of that as multiplying two numbers: (x-1) and (x-4)
if either is 0, then when we multiply we will get 0 for the top

Answer 20

in other words
if
x-1 = 0
or
x-4=0
we will get 0 up top

Answer 21

i was doing this question using another method. i just put the whole equation equal to 0

Answer 22

because to find the x intercept shouldn't y be 0?

Answer 23

yes, but the "bottom" does not matter
if you have a fraction
0/2 or 0/3 or 0/ (pick a number) you get 0
(the only time we care about the bottom is if we get 0/0 ... which is trouble)

Answer 24

so could i just put the top equal to 0?

Answer 25

yes.

Answer 26

okay so let me figure this out. i need a sec

Answer 27

i got y=4

Answer 28

you want to find the x's that make f(x) = 0
in other words, where the top
x^2 -5x + 4 =0

(x-4)(x-1)= 0

Answer 29

so its (1,4)

Answer 30

i got it thank you!

Answer 31

yes. If you want to be extra careful, be sure the bottom is not zero for x=1 or x=4
(because we don't allow 0/0)
but in this case, the bottom will not be 0 for either of those x values.

so the zeros of f(x) are at x=1 and x=4