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If 3 is one value of x for the equation x^2 7x + k = 5, where k is
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30 Mar 2022, 01:42
30 Mar 2022, 01:42
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If 3 is one value of x for the equation x^2 − 7x + k = −5, where k is a constant, what is the other solution?
A. 2
B. 4
C. 5
D. 6
E. 12
A. 2
B. 4
C. 5
D. 6
E. 12
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Re: If 3 is one value of x for the equation x^2 7x + k = 5, where k is
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30 Mar 2022, 02:17
30 Mar 2022, 02:17
1
This looks a lot harder than it really is.
First, just look at the quadratic, but set it equal to zero first:
x^2 - 7x + (k + 5) = 0
We are told that one of the solutions for x = 3, so that means that this must split this way:
(x-3) (??) = x^2 - 7x + (k + 5)
Focus on the -7x term here: the only way we'll achieve that is if we have this:
(x-3)(x-4) = x^2 - 7x + 12
This implies, of course, that k + 5 = 12, or k = 7.
The other solution, however, is what it's asking for. We can see that x = 3 or x = 4, so the one we're not given is x = 4. The answer is B.
First, just look at the quadratic, but set it equal to zero first:
x^2 - 7x + (k + 5) = 0
We are told that one of the solutions for x = 3, so that means that this must split this way:
(x-3) (??) = x^2 - 7x + (k + 5)
Focus on the -7x term here: the only way we'll achieve that is if we have this:
(x-3)(x-4) = x^2 - 7x + 12
This implies, of course, that k + 5 = 12, or k = 7.
The other solution, however, is what it's asking for. We can see that x = 3 or x = 4, so the one we're not given is x = 4. The answer is B.
gmatclubot
Re: If 3 is one value of x for the equation x^2 7x + k = 5, where k is [#permalink]
30 Mar 2022, 02:17
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