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What is the highest integral value of 'k' for which the quad

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What is the highest integral value of 'k' for which the quad [#permalink]

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What is the highest integral value of 'k' for which the quadratic equation x^2 - 6x + k = 0 have two real and distinct roots?

A. 9
B. 7
C. 3
D. 8
E. 12
[Reveal] Spoiler: OA

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Re: What is the highest integral value of 'k' for which the quad [#permalink]

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New post 22 Aug 2013, 10:53
Asifpirlo wrote:
What is the highest integral value of 'k' for which the quadratic equation x^2 - 6x + k = 0 have two real and distinct roots?

A. 9
B. 7
C. 3
D. 8
E. 12

for a quadratic equation \(ax^2+bx+c=0\)
to have 2 different roots discriminant D must be greater than 0.
\(D =b^2-4ac\)
hence \(36-4k>0\)
\(k<9\)
so highest integral value = \(8\)
hence D
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Re: What is the highest integral value of 'k' for which the quad [#permalink]

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New post 22 Aug 2013, 22:02
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for any quadratic equation \(ax^2 + bx + c = 0\), the nature of its roots can be determined by knowing its discriminant(D). \(Discriminant = b^2 - 4ac\)

if Discriminant = 0, then Quadratic equation will have real and equal roots.
if Discriminant > 0, then Quadratic equation will have real and unequal roots.
if Discriminant < 0, then Quadratic equation will have imaginary roots.

in our case for \(x^2 - 6x + k = 0\) to have real and distinct roots, \((-6)^2 - 4k\) must be greater than zero. So we have \((-6)^2 - 4k > 0\) ----------> \(36 - 4k > 0\) --------------> \(4k < 36\) ---------> \(k < 9\) ------------> The greatest value of K will be 8.
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Re: What is the highest integral value of 'k' for which the quad [#permalink]

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New post 16 May 2015, 03:45
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Re: What is the highest integral value of 'k' for which the quad [#permalink]

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New post 18 Feb 2017, 10:52
Hello from the GMAT Club BumpBot!

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Re: What is the highest integral value of 'k' for which the quad   [#permalink] 18 Feb 2017, 10:52
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