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For what value of x between -1 and 5

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saswata4s
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For what value of x between -1 and 5 [#permalink] New post   09 Oct 2017, 10:29
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For what value of x between -1 and 5 inclusive, is the value x^2 - 7x + 10 the smallest?

(A) -1
(B) 0
(C) 2
(D) 3
(E) 5
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D
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For what value of x between -1 and 5 [#permalink] New post   09 Oct 2017, 10:37
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saswata4s wrote:
For what value of x between -1 and 5 inclusive, is the value x^2 - 7x + 10 the smallest?

(A) -1
(B) 0
(C) 2
(D) 3
(E) 5


\(x^2 - 7x + 10 = (x-5)(x-2)\)

For option A, B, C & E, this equation is either positive or 0. For Option D the equation is negative and hence the lowest

Answer D
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Re: For what value of x between -1 and 5 [#permalink] New post   13 Oct 2017, 01:45
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saswata4s wrote:
For what value of x between -1 and 5 inclusive, is the value x^2 - 7x + 10 the smallest?

(A) -1
(B) 0
(C) 2
(D) 3
(E) 5


Note that the given expression is a quadratic and its graph will be an upward facing parabola. So the minimum will be at x = -b/2a.
x = -(-7)/2*1 = 3.5
Of the given options, 3 is closest to 3.5 so that is where the expression will be minimum.
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Re: For what value of x between -1 and 5 [#permalink] New post   09 Oct 2017, 10:46
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Answer D. The equation gets simplified as (x-5)(x-2). So at 2&5, the equation is 0 so C & E options are out. Only for option D will the value be less than 0.

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Re: For what value of x between -1 and 5 [#permalink] New post   12 Oct 2017, 18:14
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saswata4s wrote:
For what value of x between -1 and 5 inclusive, is the value x^2 - 7x + 10 the smallest?

(A) -1
(B) 0
(C) 2
(D) 3
(E) 5


Let’s factor the given equation:

(x - 5)(x - 2)

We see that when x is 5 or 2, one of the factors will be 0; thus, the value of the expression is 0.

When x is -1 or 0, both factors will be negative, and thus the value of the expression is positive.

Finally, when x is 3, one factor is positive while the other is negative, and thus the value of the expression is negative.

We see, then, that the value of the expression is smallest when x = 3.

Answer: D
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Re: For what value of x between -1 and 5 [#permalink] New post   12 Oct 2017, 18:35
\(x^2\)-7x+2= (x-5)(x-2)

Put A in the above equation: (-1-5)(-1-2)= 18
Put B in the above equation: (0-5)(0-2)= 10
Put C in the above equation: (2-5)(2-2)= 0
Put D in the above equation: (3-5)(3-2)= -2 (Smallest Value)
Put E in the above equation: (5-5)(5-2)= 0

Answer: D.

Kudos please if you like my explanation!
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Re: For what value of x between -1 and 5 [#permalink] New post   21 Mar 2021, 01:10
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