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# If x^2 − kx + 24 = 0, is x = −6?

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If x^2 − kx + 24 = 0, is x = −6?  [#permalink]

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05 Nov 2014, 08:20
2
7
00:00

Difficulty:

85% (hard)

Question Stats:

42% (01:45) correct 58% (01:47) wrong based on 189 sessions

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If x^2 − kx + 24 = 0, is x = −6?

(1) (x+6) is a factor of x^2-k·x+24=0, where k is a constant, and x is a variable.

(2) (x+4) is a factor of x^2-k·x+24=0, where k is a constant, and x is a variable.

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Re: If x^2 − kx + 24 = 0, is x = −6?  [#permalink]

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05 Nov 2014, 08:24
x^2−k·x+24=0
Solving the equation we get x = -6 or -4

Statement 1)
(1) (x+6) is a factor of x^2-k·x+24=0, where k is a constant, and x is a variable.
We already know that (x+6) is a factor of equation. No new information to determine if x = -6

2) (x+4) is a factor of x^2-k·x+24=0, where k is a constant, and x is a variable.
We already know that (x+4) is a factor of equation. No new information to determine if x = -6

Combining.
(x+6) and (x+4) are factors -> No new information to determine if x = -6
hence E)
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Re: If x^2 − kx + 24 = 0, is x = −6?  [#permalink]

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05 Nov 2014, 08:36
kinjiGC wrote:
If x^2−kx+24=0, is x=−6?

(1) (x+6) is a factor of x^2-k·x+24=0, where k is a constant, and x is a variable.

(2) (x+4) is a factor of x^2-k·x+24=0, where k is a constant, and x is a variable.

Similar question to practice: if-x-2-12x-k-0-is-x-155465.html
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Re: If x^2 − kx + 24 = 0, is x = −6?  [#permalink]

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05 Nov 2014, 11:00
Hi kinjiGC ,
How did u derive the values x = -6 or x = -4 from the question stem itself ? Can u please elaborate ?
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Re: If x^2 − kx + 24 = 0, is x = −6?  [#permalink]

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23 Nov 2014, 09:01
I think it is not possible to get the solution of the equation from stem as specified by kinji:

from statement 1:
x+6 is a factor of x^2-kx+24 = 0, substitute x = -6 and we get the value of k as -10 , from this the roots of the equation
x^2-10x+24 = 0 are -4 and -6, so NSF
from statement 2:
we have the same result NSF
combined x = -4 or -6 so, NSF

E
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Re: If x^2 − kx + 24 = 0, is x = −6?  [#permalink]

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08 Oct 2017, 02:14
For x2−k·x+24=0, pairs of roots can be (-6,-4),(6,4),(-12,-2) and (-8,-3) etc.
1) We have been told that (x+6) is a root so our pair is (-6,-4). Here two values of x can be possible. Not Sufficient.
2) Same as statement 1.

1& 2 together not sufficient.
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Re: If x^2 − kx + 24 = 0, is x = −6?  [#permalink]

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25 Oct 2018, 10:09
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Re: If x^2 − kx + 24 = 0, is x = −6?   [#permalink] 25 Oct 2018, 10:09
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