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# What is the minimum value of z for which (z^2)+z-(3/4)>0

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What is the minimum value of z for which (z^2)+z-(3/4)>0 [#permalink]

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16 Feb 2006, 22:23
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What is the minimum value of z for which (z^2)+z-(3/4)>0 is not true?

(A) -5/2
(B) -3/2
(C) -1/2
(D) 1/4
(E) 1/2
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16 Feb 2006, 22:29
B? I hate inequalities... I always end up spending too much time on them. What is a good way of finding the answer without plugging in all the numbers?
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16 Feb 2006, 22:36
(z^2)+z-(3/4) = 4z^2 + 4z - 3 > 0
(2z+3)(2z-1) > 0
z>0.5

Smallest value for it not to be true = 1/2

since (2z+3)(2z-1) = 0 (and so not >0)
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16 Feb 2006, 22:49
Wilfred wouldn't it still be B though since z=-3/2 satisfies 2z+3=0 ?
Good idea multiplying both sides by 4, I gave up thinking it was too complicate to factor.....
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17 Feb 2006, 00:30
For (z^2)+z-(3/4)>0, we need z > 0.5. I took the meaning of minimum value as z=0.5. That's sufficient to fail the inequality.
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17 Feb 2006, 06:24
The question should be interpreted as this: What is the minimum value of z for which (z^2)+z-(3/4) <= 0 is true?

This is equivalent to (2z+3)(2z-1) <= 0
The solution set is -3/2<=z<=1/2
So the minimal value for z is -3/2.
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17 Feb 2006, 06:30
cattalk wrote:
B? I hate inequalities... I always end up spending too much time on them. What is a good way of finding the answer without plugging in all the numbers?

Seems that you have a pretty good grasp already. The best way for this kind of questions is to solve the inequality. You could look at this post although it only talks the very basic principles.
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17 Feb 2006, 07:12
if z =-3/2, z^2+z-(3/4) = 9/4-3/2-3/4 = (9-6-3)/4=0
if z =1/2, z^2+z-(3/4) = 1/4 + 1/2 - 3/4 = (1+2-3)/4=0
if z =1/4, z^2+z-(3/4) = 1/16 + 1/4 - 3/4 = (1+4-12)/16=-7/16 so this is not true.

seems -3/2.
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17 Feb 2006, 10:33
HongHu wrote:
The question should be interpreted as this: What is the minimum value of z for which (z^2)+z-(3/4) <= 0 is true?

This is equivalent to (2z+3)(2z-1) <= 0
The solution set is -3/2<=z<=1/2
So the minimal value for z is -3/2.

B for me too. Honored to know that at least this time my method to approach this problem was similar to HongHu.
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17 Feb 2006, 10:56
all right guys the OA is B (-3/2).

But when z =-5/2

(z^2)+z-(3/4)>0 is not True

(-5/2)^2-5/2-(3/4) = -3 (So the inequality is not true ) also -5/2 is smaller than -3/2

this question is from Quant Sticky ...Some body pls explain what i am doing wrong here
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17 Feb 2006, 12:09
(-5/2)^2-5/2-(3/4) = 3 not -3.
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18 Feb 2006, 16:29
Oppp!!
thanx HongHu
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18 Feb 2006, 19:24
Solving the inequality we get the range as

(2z-1)(2z+3) > 0

z < -3/2 or z > 1/2. Thus, the minimum value is when z = -3/2....B.
18 Feb 2006, 19:24
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# What is the minimum value of z for which (z^2)+z-(3/4)>0

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