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# If the equation x^2−6x=k has at least one solution, which of the follo

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Math Expert
Joined: 02 Sep 2009
Posts: 56304
If the equation x^2−6x=k has at least one solution, which of the follo  [#permalink]

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11 Sep 2016, 05:30
1
7
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:56) correct 37% (01:38) wrong based on 103 sessions

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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

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Re: If the equation x^2−6x=k has at least one solution, which of the follo  [#permalink]

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11 Sep 2016, 06:27
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1
x^2−6x=k
=> x^2−6x - k = 0

For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative.

b^2-4ac ≥0
=> 36 - 4*1*(-k) ≥0
=> 36 + 4k ≥0
=> k ≥ -9
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Re: If the equation x^2−6x=k has at least one solution, which of the follo  [#permalink]

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11 Sep 2016, 07:15
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1
Bunuel 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

1. b2 −4ac < 0 There are no real roots.

2. b2 −4ac = 0 There is one real root.

3. b2 −4ac > 0 There are two real roots.

so, For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative.

b^2-4ac ≥0
=> 36 - 4*1*(-k) ≥0
=> 36 + 4k ≥0
=> k ≥ -9

ans: (E)
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Re: If the equation x^2−6x=k has at least one solution, which of the follo  [#permalink]

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16 Jul 2018, 04:14
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Re: If the equation x^2−6x=k has at least one solution, which of the follo   [#permalink] 16 Jul 2018, 04:14
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