Virginia state standards of Learning Algebra problem

**vaironxxrd** · January 5th 2011, 03:17 PM

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.

**Archie Meade** · January 5th 2011, 03:21 PM

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.

**dwsmith** · January 5th 2011, 03:21 PM

Do you know how to factor?

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

$\alpha*\beta=-6$

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

**rtblue** · January 5th 2011, 03:21 PM

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: $x^2+x-12$

**Plato** · January 5th 2011, 03:42 PM

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.

**vaironxxrd** · January 5th 2011, 03:45 PM

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

**vaironxxrd** · January 5th 2011, 03:46 PM

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

**dwsmith** · January 5th 2011, 03:48 PM

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.

**Archie Meade** · January 5th 2011, 03:56 PM

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.

**Plato** · January 5th 2011, 04:26 PM

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.

**vaironxxrd** · January 5th 2011, 05:17 PM

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

**vaironxxrd** · January 5th 2011, 05:22 PM

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

**Archie Meade** · January 5th 2011, 05:23 PM

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...

**vaironxxrd** · January 5th 2011, 05:26 PM

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...

yea, i was just talking to my teacher today about this same subject.
If im not very sure . Plug the numbers in

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