Quadratic Equation factorization problem

[kashan123999]

Homework Statement

In the expression x2 + kx + 12, k is an integer and k < 0. Which of the following is a possible value of k?
(A) –13
(B) –12
(C)  –6
(D)   7

Homework Equations

I know it uses the a.c method of factorization but don't know how to use it?

The Attempt at a Solution

Tried to solve it by using discriminant that is b^2 - 4ac = 0,i have only remembered the formula of that,so couldn't remember which equation will apply here...Please can anyone explain it thoroughly and correctly in lay-man's terms

 

[Mentallic]

There must be more to this problem because "k is an integer and k < 0" being the only restriction gives us possible answers of A,B,C.

Could you please write out the question exactly as you see it written?

 

[kashan123999]

here is the copied statement from Princeton SAT review
In the expression x^2 + kx + 12, k is an integer and k < 0. Which of the following is a possible value of k?
(A) –13
(B) –12
(C)  –6
(D)   7
(E) It cannot be determined from the information given.

 

[micromass]

Clearly, (A), (B) and (C) are all possible values for k.

 

[kashan123999]

Their Answer...''To solve the question, you need to factor. This question is just a twist on the example used above. Don’t worry that we don’t know the value of k. The question said that k was an integer and that means that you probably need to consider only the integer factors of 12. The possible factors of 12 are 1 and 12, 2 and 6, and 3 and 4. Since 12 is positive and k is negative, the you’ll need subtraction signs in both factors.
The possibilities are:
x2 + kx + 12 = (x – 1)(x – 12)

x2 + kx + 12 = (x – 2)(x – 6)

x2 + kx + 12 = (x – 3)(x – 4)

If you FOIL each of these sets of factors, you’ll get:
(x – 1)(x – 12) = x2 –13x + 12

(x – 2)(x – 6) = x2 –8x + 12

(x – 3)(x – 4) = x2 –7x + 12

The correct answer is A, as −13 is the only value from above included in the answers. Of course, you didn’t need to write them all out if you started with 1 and 12 as your factors.''Please explain that in simple terms please :(

 

[micromass]

Their Answer...''To solve the question, you need to factor. This question is just a twist on the example used above. Don’t worry that we don’t know the value of k. The question said that k was an integer and that means that you probably need to consider only the integer factors of 12. The possible factors of 12 are 1 and 12, 2 and 6, and 3 and 4. Since 12 is positive and k is negative, the you’ll need subtraction signs in both factors.
The possibilities are:
x2 + kx + 12 = (x – 1)(x – 12)

x2 + kx + 12 = (x – 2)(x – 6)

x2 + kx + 12 = (x – 3)(x – 4)

If you FOIL each of these sets of factors, you’ll get:
(x – 1)(x – 12) = x2 –13x + 12

(x – 2)(x – 6) = x2 –8x + 12

(x – 3)(x – 4) = x2 –7x + 12

The correct answer is A, as −13 is the only value from above included in the answers. Of course, you didn’t need to write them all out if you started with 1 and 12 as your factors.''


Please explain that in simple terms please :(

Well, that makes no sense. I guess it's a typo and the question is incomplete. It should be

In the expression $x^2 + kx + 12$, $k$ is an integer and $k < 0$. If the roots of the expression are integers, then which of the following is a possible value of k?

 

[sjb-2812]

It would be good to see "the example above"; but perhaps it says something about factors being integers or something. Nothing fundamentally wrong with any negative number.

 

[kashan123999]

Well, that makes no sense. I guess it's a typo and the question is incomplete. It should be

In the expression $x^2 + kx + 12$, $k$ is an integer and $k < 0$. If the roots of the expression are integers, then which of the following is a possible value of k?

nah it is mentioned that k is integer hence root is integer...is it the right info?

 

[kashan123999]

It would be good to see "the example above"; but perhaps it says something about factors being integers or something. Nothing fundamentally wrong with any negative number.

thank you...btw can you comprehend me the meaning of that statement,want to transform in it in mathematical form..."A Baseball team won 54 more games than it lost"

 

[sjb-2812]

nah it is mentioned that k is integer hence root is integer...is it the right info?

Not necessarily, for instance the equation $x^{2}-9x-12$ has integer k here; and roots $\frac{9}{2}\pm\sqrt{\frac{33}{2}}$

 

[Mentallic]

nah it is mentioned that k is integer hence root is integer...is it the right info?

No, because k=-2 is an integer but the roots of $x^2-2x+12$ are not integers. In fact, if k is any negative number other than -7,-8 or -13, then the quadratic won't have integer roots.

thank you...btw can you comprehend me the meaning of that statement,want to transform in it in mathematical form..."A Baseball team won 54 more games than it lost"

Which part of it don't you understand? You'll also need to be more detailed with your baseball team question.

 

[kashan123999]

Not necessarily, for instance the equation $x^{2}-9x-12$ has integer k here; and roots $\frac{9}{2}\pm\sqrt{\frac{33}{2}}$

ahan so -13 is surely the right answer but how to evaluate that using discriminants ?

 

[Mentallic]

ahan so -13 is surely the right answer but how to evaluate that using discriminants ?

The discriminant is really only helpful in telling you how many roots the quadratic has. This doesn't mean it can't be done, but it's beyond your understanding at the moment.

 

[kashan123999]

The discriminant is really only helpful in telling you how many roots the quadratic has. This doesn't mean it can't be done, but it's beyond your understanding at the moment.

so any alternative method to solve the question

 

[Mentallic]

Take each value of k given in the options and test to see if you can factorize it.

Can you factorize $x^2-13x+12$ ? What about $x^2-12x+12$ ? etc.

And obviously ignore k=7 since the question said that k<0.