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x is any non-negative integer

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Carcass
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x is any non-negative integer [#permalink] New post   27 Jan 2021, 06:14
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x is any non-negative integer

Quantity A
Quantity B
The minimum value of \(4x^2+1\)
The minimum value of \(5x^2+1\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation
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C
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KarunMendiratta
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Re: x is any non-negative integer [#permalink] New post   30 May 2021, 00:28
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Carcass wrote:
x is any non-negative integer

Quantity A
Quantity B
The minimum value of \(4x^2+1\)
The minimum value of \(5x^2+1\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation


Both the equations given here are Quadratic Functions (Parabola)

The minimum value i.e. the y-value (only when a > 0) of a Parabola occurs at it's vertex

x-coordinate of the vertex = \(\frac{-b}{2a}\), which is same for both the equations

\(4x^2 + 0x + 1\)
x-coordinate of the vertex = \(\frac{-0}{8} = 0\)

\(5x^2 + 0x + 1\)
x-coordinate of the vertex = \(\frac{-0}{10} = 0\)

Now, on plugging the x-coordinates back into the equation, we have same y-coordinates as 1

Col. A: 1
Col. B: 1

Hence, option C

You can also try to draw the graph of both the functions and notice that they have same vertex!
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Parabolas.png
Parabolas.png [ 92.12 KiB | Viewed 2231 times ]

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Re: x is any non-negative integer [#permalink] New post   27 Jan 2021, 07:32
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x is a non-negative, so \(x>=0\)

We need min value so we will take x = 0

Qt A = Qt B = 1

Answer C
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Re: x is any non-negative integer [#permalink] New post   29 May 2021, 18:36
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Carcass wrote:
x is any non-negative integer

Quantity A
Quantity B
The minimum value of \(4x^2+1\)
The minimum value of \(5x^2+1\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation


In Quantity A , \(4x^2 + 1 \) and similarly in \(5x^2 + 1\) Quantity B



subtracting 1 from both sides,
\(4x^2 \) in Quantity A and \(5x^2\) in Quantity B


since, \(x^2 \)is always positive, hence , we can safely divide by it.
then 4 remain in quantity A and 5 remain Quantity B.

Hence, quantity B is greater..
Carcass sir, please add OA for this particular question.
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Re: x is any non-negative integer [#permalink]
29 May 2021, 18:36
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