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24x^2 + bx + c=(dx+e)(fx+g)
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25 Dec 2019, 00:54
25 Dec 2019, 00:54
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Question Stats:
70% (01:48) correct
29% (02:05) wrong based on 201 sessions
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\(24x^2 + bx + c=(dx+e)(fx+g)\)
\(b,c,d,e,f,\) and \(g\) are integers
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
\(b,c,d,e,f,\) and \(g\) are integers
Quantity A |
Quantity B |
\(d+f\) |
\(26\) |
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: 24x^2 + bx + c=(dx+e)(fx+g)
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04 Apr 2020, 06:31
04 Apr 2020, 06:31
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Carcass wrote:
\(24x^2 + bx + c=(dx+e)(fx+g)\)
\(b,c,d,e,f,\) and \(g\) are integers
\(b,c,d,e,f,\) and \(g\) are integers
Quantity A |
Quantity B |
\(d+f\) |
\(26\) |
Given: 24x² + bx + c =(dx + e)(fx + g)
Use FOIL to expand the right side to get: 24x² + bx + c = dfx² + gdx + efx + eg
On the left side, the coefficient of x² is 24.
On the right side, the coefficient of x² is df
So, we can conclude that: 24 = df
At this point, the key word in the given information is that d and f are INTEGERS
Since we know that 24 = df, we can see that there aren't many pairs of INTEGER values that have a product of 24.
We get: (1)(24) = 24, (2)(12) = 24, (3)(8) = 24, and (4)(6) = 24
Quantity A = d + f
Notice that the MAXIMUM possible value of d + f occurs when the two numbers are 1 and 24, in which case we get us some of 25
This means d + f will always be less than 26
Answer: B
Cheers,
Brent
General Discussion
Re: 24x^2 + bx + c=(dx+e)(fx+g)
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25 Dec 2019, 01:30
25 Dec 2019, 01:30
1
You can solve this very easily. Since 24x2+bx+c can be expressed as (x-x1)(x-x2), you can consider d and f equal to 1. Therefore d+f=2 < 26. Regards!
