Question:
If x(x - 5)(x + 2) = 0, is x negative?
1) x² – 7x ≠ 0
(2) x² –2x –15 ≠ 0
Spolier:QA:C
Solution:
x(x - 5)(x + 2) = 0 => x= 0 or 5 or -2
(1) x^2 – 7x ≠ 0 => x(x-7) ≠ 0
=> x ≠ 0 & x ≠ 7.
So x=5 or -2 INSUFFICIENT
(2) x^2 –2x –15 ≠ 0
=> (x-5)(x+3)≠ 0
=> x ≠ 5 & x ≠ -3
Therefore x=0 or -2 INSUFFICIENT
Combining,
x ≠ 0, x ≠ 5 => x=-2 SUFFICIENT
The correct answer is C.
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