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\(x(x - 5)(x + 2) = 0\) --> \(x=0\) 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.

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

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04 Jul 2013, 08:23

For the given equation to be equal to 0 x must either equal 0, 5 or -2.

Statement 1: Tells us that x cannot equal 0 or 7. But it could equal 5 or -2. Not sufficient Statement 2: Tells us that x cannot equal 5 or -3. But it could equal -2 or 0.

Taken together x cannot equal 0 or 5. Therefore, x must equal -2. Answer: C