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If x^2 - 7x + |k| = 0 has real roots. How many integer values can 'k'

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Director
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Joined: 20 Jul 2017
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Location: India
Concentration: Entrepreneurship, Marketing
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If x^2 - 7x + |k| = 0 has real roots. How many integer values can 'k'  [#permalink]

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New post 07 Aug 2019, 05:31
3
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

33% (01:40) correct 67% (02:09) wrong based on 50 sessions

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If x^2 - 7x + |k| = 0 has real roots. How many integer values can 'k' take?

A. 0
B. 12
C. 13
D. 24
E. 25
Senior Manager
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Joined: 16 Jan 2019
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Location: India
Concentration: General Management
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Re: If x^2 - 7x + |k| = 0 has real roots. How many integer values can 'k'  [#permalink]

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New post 07 Aug 2019, 08:11
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1
The equation \(ax^2+bx+c=0\) has real roots when \(b^2-4ac>0\)

In the equation \(x^2 - 7x + |k| = 0\), \(a=1\), \(b=-7\), \(c=|k|\)

Therefore \((-7)^2-4(1)(|k|)>0\)

\(49-4|k|>0\)
\(4|k|<49\)
\(|k|<12.25\)

\(-12.25<k<12.25\)

So \(k\) can take all integer values from -12 to 12 that is 25 values

Answer is (E)

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Re: If x^2 - 7x + |k| = 0 has real roots. How many integer values can 'k'   [#permalink] 07 Aug 2019, 08:11
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If x^2 - 7x + |k| = 0 has real roots. How many integer values can 'k'

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