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

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Director
Joined: 20 Jul 2017
Posts: 633
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
If x^2 - 7x + |k| = 0 has real roots. How many integer values can 'k'  [#permalink]

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07 Aug 2019, 05:31
3
00:00

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
Joined: 16 Jan 2019
Posts: 409
Location: India
Concentration: General Management
WE: Sales (Other)
Re: If x^2 - 7x + |k| = 0 has real roots. How many integer values can 'k'  [#permalink]

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07 Aug 2019, 08:11
3
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

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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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