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# If x(x - 5)(x + 2) = 0, is x negative?

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If x(x - 5)(x + 2) = 0, is x negative? [#permalink]

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10 May 2009, 11:09
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If x(x - 5)(x + 2) = 0, is x negative?

(1) x^2 – 7x ≠ 0
(2) x^2 –2x –15 ≠ 0

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-x-5-x-2-0-is-x-negative-89304.html
[Reveal] Spoiler: OA

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Re: If x(x - 5)(x + 2) = 0, is x negative? [#permalink]

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12 May 2009, 04:07
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vaivish1723 wrote:
If x(x-5)(x+2)=0 is x negative?
1.x^2-7x is not equal to 0
2. x^2-2x-15 is not equal to O.

1. x^2-7x is not equal to 0
x(x-7) is not equal to 0. so x is neither 0 nor 7. insuff.

2. x^2-2x-15 is not equal to O.[/quote]
x^2 - 2x - 15 is not equal to 0.
(x^2 - 5x + 3x - 15) is not equal to 0.
(x - 5) (x + 3) is not equal to 0.
x is neither 5 nor -3.

Togather x must be -2 to have x (x-5) (x+2) = 0. suff.

C.
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Re: If x(x - 5)(x + 2) = 0, is x negative? [#permalink]

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14 May 2009, 13:06
vaivish1723 wrote:
IF x(X-5)(X+2)=0 is x negative?
1.x sq.2-7x is not equal to 0
2. x2-2x-15 is not equal to O.

Fact: $$x(x-5)(x+2)=0$$
Question:( x<0 )?

Interpret fact to get that x=0,5 or -2, in the first 2 cases we have NO, in the last one we have a YES.

So we need more data.

(1) $$x*sqrt(7x) != 0$$ (correct me if I read this wrong)
This means that x != 0 & that sqrt(7x) != 0. I don't think this is an Official question (GRRRR) or a very
poorly formulate one, but we can't test x=-2 as the square root of a negative number is a complex number... So if we can use complex numbers, insufficient, and if we aren't allowed to take the square root of a negative number, sufficient, as X can only be 5. But I'm going to go with Insufficient.

(2) $$x^2 - 2x - 15 != 0$$
$$x^2 - 5x + 3x - 15 != 0$$
$$x(x - 5) + 3(x - 5) != 0$$
$$(x-5)(x+3) !=0$$
So X can't be 5 or -3, but it can still be 0 or -2. Insufficient.

(1&2)
From original equation: x=0,5,-2
1 eliminates 0
2 eliminates 5
Only x=-2 remains

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Re: If x(x - 5)(x + 2) = 0, is x negative? [#permalink]

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19 Dec 2014, 00:20
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Re: If x(x - 5)(x + 2) = 0, is x negative? [#permalink]

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19 Dec 2014, 02:54
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If x(x - 5)(x + 2) = 0, is x negative?

$$x(x - 5)(x + 2) = 0$$ --> $$x=0$$ or $$x=5$$ or $$x=-2$$. Question is $$x<0$$ or is $$x=-2$$?

(1) x^2 – 7x ≠ 0 --> $$x(x-7)\neq{0}$$--> $$x\neq{0}$$ and $$x\neq{7}$$, so $$x$$ can be 5 or -2 (from the stem as $$x=0$$ is out). Not sufficient.

(2) x^2 –2x –15 ≠ 0 --> $$(x+3)(x-5)\neq{0}$$ --> $$x\neq{-3}$$ and $$x\neq{5}$$, so $$x$$ can be 0 or -2 (from the stem as $$x=5$$ is out). Not sufficient.

(1)+(2) As $$x=0$$ and $$x=5$$ are out, only value left is $$x=-2$$, so $$x$$ is negative. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-x-5-x-2-0-is-x-negative-89304.html
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Re: If x(x - 5)(x + 2) = 0, is x negative?   [#permalink] 19 Dec 2014, 02:54
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