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# What is the minimum value of z for which z^2 + z - 3/4 > 0 is not true

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Re: What is the minimum value of z for which z^2 + z - 3/4 > 0 is not true [#permalink]

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29 Oct 2011, 03:53
These kind of questions need to be solved from substituting options and i got the answer A
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Re: What is the minimum value of z for which z^2 + z - 3/4 > 0 is not true [#permalink]

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29 Oct 2011, 05:33
cdaat wrote:
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

$$z^2+z-\frac{3}{4}>0$$

$$\frac{4z^2+4z-3}{4}>0$$

$$4z^2+4z-3>0$$

$$4z^2+6z-2z-3>0$$

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

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

Roots:
+1/2, -3/2

Means the equation will be true for:
z>+1/2
z<-3/2

OR, the equation will NOT hold true for

-3/2<=z<=1/2

Minimum of the range= -3/2

Ans: "B"
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Re: What is the minimum value of z for which z^2 + z - 3/4 > 0 is not true [#permalink]

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08 Aug 2015, 05:03
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Re: What is the minimum value of z for which z^2 + z - 3/4 > 0 is not true [#permalink]

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24 Apr 2016, 22:26
If you don't want spend time solving this, just substitute the numbers.

First sort them in order:
A)
(-5/2)^2+(-5/2)-3/4>0
25/4-10/4-3/4>0
12/4>0 True so A is not the answer

B)
(-3/2)^2+(-3/2)-3/4>0
9/4-6/4-3/4>0
0>0 Not true
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Re: What is the minimum value of z for which z^2 + z - 3/4 > 0 is not true [#permalink]

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06 May 2016, 21:06
What is the minimum value of z for which z^2 + z - 3/4 > 0 is not true?

means that we solve z^2+z-3/4=<0

backsolving gives B
Re: What is the minimum value of z for which z^2 + z - 3/4 > 0 is not true   [#permalink] 06 May 2016, 21:06

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