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What is the value of x, for which the quadratic expression, ..........

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What is the value of x, for which the quadratic expression, ..........  [#permalink]

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New post 16 Jan 2019, 02:11
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

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

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Re: What is the value of x, for which the quadratic expression, ..........  [#permalink]

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New post 16 Jan 2019, 02:36
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

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Re: What is the value of x, for which the quadratic expression, ..........  [#permalink]

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New post 16 Jan 2019, 02:42
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
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Re: What is the value of x, for which the quadratic expression, ..........  [#permalink]

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New post 16 Jan 2019, 04:56
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

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Ans: A
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Re: What is the value of x, for which the quadratic expression, ..........  [#permalink]

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New post 18 Jan 2019, 01:38

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.

Answer: A

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