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

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Bunuel
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If x^2 - 7x + |k| = 0 has real roots. How many integer values can 'k' [#permalink] New post   31 Jan 2022, 08:15
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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
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E
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If x^2 - 7x + |k| = 0 has real roots. How many integer values can 'k' [#permalink] New post   31 Jan 2022, 08:29
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For real roots, the Discriminant value must be greater than or equal to zero.

D \(= (-7)^2 - 4|K| = 49 - 4|K| \geq 0 \)

\(|K| \leq 12.25\)

Possible values of K \([-12, 12]\)

Count \(= 24+1 = 25\)

Hence, answer is E (25)
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Re: If x^2 - 7x + |k| = 0 has real roots. How many integer values can 'k' [#permalink] New post   25 Nov 2022, 23:17
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Asked: If \(x^2 - 7x + |k| = 0\) has real roots. How many integer values can 'k' take?

For real roots, discrimant should be >=0
49 - 4|k| >=0
|k| <= 49/4 = 12.25
k is all integers from -12 to 12 i.e. 25 values

IMO E
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Re: If x^2 - 7x + |k| = 0 has real roots. How many integer values can 'k' [#permalink] New post   15 Jul 2023, 03:25
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↧↧↧ Detailed Video Solution to the Problem ↧↧↧




Given that \(x^2 - 7x + |k| = 0\) has real roots and we need to find How many integer values can 'k' take

Any quadratic equation, \(ax^2 + bx + c = 0\) will have real roots when the Determinant, D ≥ 0. Where D is given by
D = \(B^2 - 4ac\) ≥ 0

Here we have, a = 1, b = -7 and c = |k|
=> \((-7)^2 - 4*1*|k|\) ≥ 0
=> 49 - 4|k| ≥ 0
=> |k| ≤ \(\frac{49}{4}\) (=12.25)
=> -12.25 ≤ k ≤ 12.25
=> K can take values from -12 to 12 = 12 -(-12) + 1 = 25 values

So, Answer will be E
Hope it helps!

Watch the following video to learn the Basics of Absolute Values

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gmatclubot
Re: If x^2 - 7x + |k| = 0 has real roots. How many integer values can 'k' [#permalink]
15 Jul 2023, 03:25
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