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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3074
What is the value of x, for which the quadratic expression, ..........  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 75% (01:43) correct 25% (01:22) wrong based on 76 sessions

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What is the value of x, for which the quadratic expression, $$x^2 + 16x + 100$$, takes the minimum possible value?

A. -8
B. -4
C. 0
D. 4
E. 8

To read all our articles: Must read articles to reach Q51

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GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 4987
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: What is the value of x, for which the quadratic expression, ..........  [#permalink]

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Use plug in technique
out of given options a -8 gives min value i.e 36
IMO A

EgmatQuantExpert wrote:
What is the value of x, for which the quadratic expression, $$x^2 + 16x + 100$$, takes the minimum possible value?

A. -8
B. -4
C. 0
D. 4
E. 8

To read all our articles: Must read articles to reach Q51

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Manager  B
Joined: 01 May 2017
Posts: 82
Location: India
Re: What is the value of x, for which the quadratic expression, ..........  [#permalink]

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x2+16x+100

1) by optional verification
-8 has the least value

2) Differentiating equation w.r.t x, to get the min
2x+16 = 0
x = -8

Option A is correct
Senior Manager  G
Joined: 13 Feb 2018
Posts: 453
GMAT 1: 640 Q48 V28 Re: What is the value of x, for which the quadratic expression, ..........  [#permalink]

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If we observe carefully:
$$x^2$$+16x+100=$$x^2$$+16x+64+36=$$(x+8)^2$$+36
As $$(x+8)^2$$ minimum value can be 0
$$(x+8)^2$$=0
x=-8

Imo
Ans: A
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3074
Re: What is the value of x, for which the quadratic expression, ..........  [#permalink]

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Solution

Given:
• A quadratic expression, $$x^2 + 16x + 100$$

To find:
• The minimum value of the given expression

Approach and Working:
• $$x^2 + 16x + 100 = x^2 + 16x + + 64 + 36 = (x^2 + 2 * 8 * x + 8^2) + 36$$
• $$(x^2 + 2 * 8 * x + 8^2) + 36$$ can be written as $$(x + 8)^2 + 36$$

The minimum value of $$(x + 8)^2 = 0$$, since, it cannot be negative for any value of x.
• Thus, the minimum value of $$x^2 + 16x + 100 = (x + 8)^2 + 36 = 0 + 36 = 36$$
• And, it occurs when x + 8 = 0

Therefore, x = -8

Hence the correct answer is Option A.

_________________ Re: What is the value of x, for which the quadratic expression, ..........   [#permalink] 18 Jan 2019, 01:38
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