Math Help - Virginia state standards of Learning Algebra problem

1. Virginia state standards of Learning Algebra problem

Hello Guys i just can't understand this question because i forgot much of my algebra's problem.. and as you can see this one has no explanation so if you guys can explain why is 3 the right answer ( got it after you do the problem wrong)
and give me some examples to solve if you guys can.

2. Originally Posted by vaironxxrd
Hello Guys i just can't understand this question because i forgot much of my algebra's problem.. and as you can see this one has no explanation so if you guys can explain why is 3 the right answer ( got it after you do the problem wrong)
and give me some examples to solve if you guys can.

$f(x)=x^2-x-6$

$f(x)=0$

$x^2-x=6\Rightarrow\ x(x-1)=6$

The factors of 6 that differ by 1 are ?
There is a positive and negative solution.

3. Do you know how to factor?

$(x\pm\alpha)(x\pm\beta)=0$

$\alpha*\beta=-6$

$x\beta\pm x\alpha=-x$

4. Factor:

$\displaystyle x^2-x-6=(x-3)(x+2)$

We are finding the zeros of this function, so we set it equal to zero.

$(x-3)(x+2)=0$

By the zero product property, either x-3 or x+2 can be zero.

we have x-3=0 and x+2=0

solving for x, we get x=3, x=-2

Here, try the following problem:

Find both zeros of: $x^2+x-12$

5. I am not sure what you expect us to do for you.
But this is the answer to your question: $f(3)=0$.
That is why 3 is the correct answer.

Now if you do not understand why, then that is a different matter.
Sometimes we all must suffer from what we have forgotten.

6. I don't like all of you said i am suffering the consequences

7. Originally Posted by Plato
I am not sure what you expect us to do for you.
But this is the answer to your question: $f(3)=0$.
That is why 3 is the correct answer.

Now if you do not understand why, then that is a different matter.
Sometimes we all must suffer from what we have forgotten.
Yea Im suffering the consequences for moving state

8. Originally Posted by vaironxxrd
I don't like all of you said i am suffering the consequences
Only one person said that not all.

Regardless of what state you are reside, you need to know how to solve polynomials in basic math.

9. I felt it better to use a straightforward method before introducing factoring and so on.
There are a few ways to solve.

$3$ and $-2$ are the two possible answers.

Here is an explanation of why 3 is an answer.

If two values are equal, then when we subtract them the answer is zero.

$6-6=0$

$\left(x^2-x\right)-6=0$

Therefore

$x^2-x=6$

$x^2=x(x)$

so $x(x)-x(1)=6$

Factor as x is common

$x(x-1)=6$

The factors of 6 that differ by 1 are 3 and 2.
Therefore x is 3 and (x-1) is 2.

However $(-3)(-2)=6$

and so $x=-2$ and $x-1=-3$ is an alternative.

If that makes sense, you could try $(x-3)(x+2)=x^2-x-6$ later.

10. Frankly I have written for this kind of test, albeit in a different state in the US.
I will tell you the objective of the question.
You are given an option of say five different choices.
Probability three of which are wildly off.
So that leaves only two to check. Which gives $f(a)=0~?$

What this tests is your understanding of the meaning of a zero of a function?

If you have to actually take time to solve the equation, then that docks time from you on the rest of the test. So understanding the basic concepts improves your overall score.

11. Originally Posted by dwsmith
Only one person said that not all.

Regardless of what state you are reside, you need to know how to solve polynomials in basic math.
Sorry i meant " Like all of you said" And yea one person said that

12. Originally Posted by Plato
Frankly I have written for this kind of test, albeit in a different state in the US.
I will tell you the objective of the question.
You are given an option of say five different choices.
Probability three of which are wildly off.
So that leaves only two to check. Which gives $f(a)=0~?$

What this tests is your understanding of the meaning of a zero of a function?

If you have to actually take time to solve the equation, then that docks time from you on the rest of the test. So understanding the basic concepts improves your overall score.
oh ok i understand, i am now trying my hardest on this kind of stuff like Algebra geometry, and focusing on practicing my weak points in math

13. In the case of your question,
were you given values from which to choose ?

In that case, you only need place the values into the equation to see which one gives you zero,
as Plato showed.

$x^2-x-6=0$

If x=2

$2^2-2-6=(4-2)-6=2-6$ which is not zero.

If x=5

$5^2-5-6=(25-5)-6=20-6$ which is not zero.

If x=3

$3^2-3-6=(9-3)-6=6-6$

and that is zero.

No need for factoring...

14. Originally Posted by Archie Meade
In the case of your question,
were you given values from which to choose ?

In that case, you only need place the values into the equation to see which one gives you zero,
as Plato showed.

$x^2-x-6=0$

If x=2

$2^2-2-6=(4-2)-6=2-6$ which is not zero.

If x=5

$5^2-5-6=(25-5)-6=20-6$ which is not zero.

If x=3

$3^2-3-6=(9-3)-6=6-6$

and that is zero.

No need for factoring...