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a and b are roots of the equation x2 - px + 12 = 0. If the difference

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a and b are roots of the equation x2 - px + 12 = 0. If the difference  [#permalink]

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New post 24 Nov 2019, 23:08
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A
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Difficulty:

  95% (hard)

Question Stats:

22% (02:20) correct 78% (02:44) wrong based on 27 sessions

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a and b are roots of the equation \(x^{2}\) - px + 12 = 0. If the difference between the roots is at least 12, what is the range of values p can take?

A. (0, 2)
B. (-2, 2)
C. (-∞, -2) or (-2, 2)
D. (-2, 0)
E. (2, 12)
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a and b are roots of the equation x2 - px + 12 = 0. If the difference  [#permalink]

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New post Updated on: 30 Nov 2019, 11:37
a+b=p
ab=12

Also, a-b ≥ 12

a^2+b^2-2ab ≥ 144
a^2+b^2+2ab -4ab ≥ 144

(a+b)^2 - 48 ≥ 144
(a+b)^2 ≥ 192

\(|a+b| ≥ 8\sqrt{3}\)

p ∈ (-∞, \(-8\sqrt{3}\)] U [\(8\sqrt{3}\), ∞)

OA is not correct imo. Between -2 and 2, equation doesn't even has real roots.





DisciplinedPrep wrote:
a and b are roots of the equation \(x^{2}\) - px + 12 = 0. If the difference between the roots is at least 12, what is the range of values p can take?

A. (0, 2)
B. (-2, 2)
C. (-∞, -2) or (-2, 2)
D. (-2, 0)
E. (2, 12)

Originally posted by nick1816 on 25 Nov 2019, 14:56.
Last edited by nick1816 on 30 Nov 2019, 11:37, edited 1 time in total.
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Re: a and b are roots of the equation x2 - px + 12 = 0. If the difference  [#permalink]

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New post 30 Nov 2019, 07:40
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Re: a and b are roots of the equation x2 - px + 12 = 0. If the difference   [#permalink] 30 Nov 2019, 07:40
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a and b are roots of the equation x2 - px + 12 = 0. If the difference

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