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If the equation x^2−6x=k has at least one solution, which of the follo
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13 Jan 2022, 09:09
13 Jan 2022, 09:09
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63% (01:24) correct
36% (01:31) wrong based on 22 sessions
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If the equation x² - 6x = k has at least one solution, which of the following must be true?
A. k > 9
B. k < −9
C. k = 9
D. k ≤ 9
E. k ≥ −9
A. k > 9
B. k < −9
C. k = 9
D. k ≤ 9
E. k ≥ −9
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Re: If the equation x^2−6x=k has at least one solution, which of the follo
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13 Jan 2022, 11:00
13 Jan 2022, 11:00
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Carcass wrote:
If the equation x^2−6x=k has at least one solution, which of the following must be true?
A. k > 9
B. k < −9
C. k = 9
D. k ≤ 9
E. k ≥ −9
A. k > 9
B. k < −9
C. k = 9
D. k ≤ 9
E. k ≥ −9
Key property: If a quadratic equation is presented in the form ax² + bx + c = 0, then:
- The equation will have no solutions if b² - 4ac < 0
- The equation will have 1 solution if b² - 4ac = 0
- The equation will have 2 solutions if b² - 4ac > 0
Given: x² - 6x = k
Subtract k from both sides: x² - 6x - k = 0
At this point we can see that a = 1, b = -6 and c = -k
If the equation has at least one solution then we can conclude b² - 4ac ≥ 0
Plug a = 1, b = -6 and c = -k into the inequality to get: (-6)² - (4)(1)(-k) ≥ 0
Simplify: 36 + 4k ≥ 0
Subtract 36 from both sides: 4k ≥ -36
Divide both sides by 4 to get: k ≥ -9
Answer: E
Re: If the equation x^26x=k has at least one solution, which of the follo
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23 Sep 2024, 22:49
23 Sep 2024, 22:49
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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