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# If z - 4z > 5 then which of the following is always true

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Intern
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If z - 4z > 5 then which of the following is always true [#permalink]

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26 May 2005, 03:38
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If zÂ² - 4z > 5 then which of the following is always true

A) z > -5
B) z < 5
C) z > -1
D) z < 1
E) z < -1
Director
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26 May 2005, 04:01
Z^2-4z-5>0 then (z-5)(z+1)>0 or Z is in interval [Z>5 and Z<-1] you can figure it out yourself.
Director
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26 May 2005, 14:43
E.

This one can be solved very quickly, no scratch paper needed, all that has to be done is to visualize parabola z^2 - 4z - opening up, crosses z at 0 and 4.

Last edited by sparky on 26 May 2005, 15:39, edited 1 time in total.
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26 May 2005, 14:59
E)...

z^2-4z-5>0 => (z-5)(z+1)>0 => z>5 and z>-1 or z<5 and z<-1
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Intern
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27 May 2005, 12:43
Why isn't it C?

I don't see how :

(z-5)(z+1)>0

translates into z < -1. I thought the sign only gets flipped when multiplying or dividing by a negative number.

example)
-2x > 6
x < -3

Here we're just subtracting it to the other side. no?

z+1 > 0
z > -1
27 May 2005, 12:43
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# If z - 4z > 5 then which of the following is always true

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