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x is any non-negative integer
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27 Jan 2021, 06:14
27 Jan 2021, 06:14
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x is any non-negative integer
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
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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Re: x is any non-negative integer
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30 May 2021, 00:28
30 May 2021, 00:28
1
Carcass wrote:
x is any non-negative integer
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
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!
Attachments
Parabolas.png [ 92.12 KiB | Viewed 2615 times ]
General Discussion
Re: x is any non-negative integer
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27 Jan 2021, 07:32
27 Jan 2021, 07:32
2
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
We need min value so we will take x = 0
Qt A = Qt B = 1
Answer C
