Question

What are the zeros of the function f(x) = (3x^2 + 9x + 6) / (3x - 6) ?

–1

1

2

–2

Answer 1

How do you exactly find the zeros? Cause it has to be one of those above?

Answer 2

1

Answer 3

According to the intermediate value theorem, you can find two points in which the function is once positive and one negative so you know that there must be at least one point where your function is zero. Now, your function is a parabola, put it equal to zero and fint the solutions.

0 = (3x^2 + 9x + 6) / (3x - 6)

x= -2 x= -1

Now, I have no idea why your book gives out just one possible answer. As a matter of fact it is a 2degree equation, uhm... o,o

Answer 4

Yeah I'm not sure why they only put one, but I agree there should be two zeros o.O

Answer 5

But how did you get rid of the denominator?

Answer 6

Just multiply both members for the denominator. So you can just take it off since on the other side there is a zero.

Answer 7

Multiply?
This is where I got up to:

3(x + 1) (x + 2)
_______________
3 (x - 1)

Answer 8

\[\frac{a}{b} = 0\]

\[b *\frac{a}{b} = 0*b\]

\[\frac{a}{1} = 0 \rightarrow a = 0\]

Answer 9

Are you sure that is what you are suppose to do?

Answer 10

Find the zeros of a function means to find the points in which a function equals to zero.
We know these points to exist, as I explained before, since the function gets a positive and a negative value in two different points, so there must be AT LEAST one, where it is zero.
So... f(x) = 0
You solve such equation, you get the points you wanted to find.

I think this is the right logic.

Answer 11

Yeah it's just that my lesson shows that I should cancel out something, Idk, but they didnt teach me the multiplying part :( I graphed it on this program called geogebra and it told me -2 and -1 also

Answer 12

Oh wow.... I typed in the equation wrong it is suppose to be
f(x) = (3x^2 + 9x + 6) / (3x - 3)

Answer 13

doesnt matter. the zeroes are the same

Answer 14

zeroes of a function are the points at which the function value is 0. so equate f(x) = 0 and solve

Answer 15

@dhatraditya I did so up there, but I find two solutions, since it's a 2nd degree equation, his book reports just one solution. And I cannot really understand why, I find my reasoning to be correct, but well. o_O

Answer 16

But can you show the work? if you dont mind?

Answer 17

Check the attachment.

Answer 18

Oh ok ^^ thank you for the help