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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a
[#permalink]
10 Nov 2021, 04:04
10 Nov 2021, 04:04
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Question Stats:
66% (01:12) correct
33% (01:58) wrong based on 3 sessions
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If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a positive number t?
A. 2√15
B. 4√15
C. 3√13
D. 4√13
E. 6√15
A. 2√15
B. 4√15
C. 3√13
D. 4√13
E. 6√15
If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a
[#permalink]
11 Nov 2021, 03:13
11 Nov 2021, 03:13
A parabola being tangent to the x-axis means it only has one root and f(x) = 0 and \(b^2 - 4ac = 0\)
\(3x^2 - tx + 5 = 0\)
\(a = 3, b = -t, c = 5\)
\(b^2 - 4ac = 0\)
\((-t)^2 - 4(3)(5) = 0\)
\(t^2 = 4(15)\)
\(t = +2\sqrt{15}\) and \(-2\sqrt{15}\)
Since the question asks for positive value of \(t\),
\(t = +2\sqrt{15}\)
Hence, Answer is A
\(3x^2 - tx + 5 = 0\)
\(a = 3, b = -t, c = 5\)
\(b^2 - 4ac = 0\)
\((-t)^2 - 4(3)(5) = 0\)
\(t^2 = 4(15)\)
\(t = +2\sqrt{15}\) and \(-2\sqrt{15}\)
Since the question asks for positive value of \(t\),
\(t = +2\sqrt{15}\)
Hence, Answer is A
gmatclubot
If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a [#permalink]
11 Nov 2021, 03:13
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