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How many real solutions exist for the equation x2 – 11|x| - 60 = 0? 3

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How many real solutions exist for the equation x2 – 11|x| - 60 = 0? 3  [#permalink]

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New post 30 Dec 2018, 12:23
5
8
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

48% (01:34) correct 52% (01:50) wrong based on 157 sessions

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How many real solutions exist for the equation x^2 – 11|x| - 60 = 0?

A 3
B 2
C 1
D 4
E 0

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Re: How many real solutions exist for the equation x2 – 11|x| - 60 = 0? 3  [#permalink]

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New post 30 Dec 2018, 12:33
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2
Given that x^2 – 11|x| - 60 = 0

Case 1:
When, x is greater or equal to zero, then |x| = x
x^2 – 11x - 60 = 0
x^2 – 15x + 4x - 60 = 0
(x - 15)(x + 4) = 0
x = 15, or -4
However, the initial condition is that x must be greater or equal to zero. Hence, only one solution from Case 1, i.e. x = 15

Case 2:
When, x is less zero, then |x| = - x
x^2 + 11x - 60 = 0
x^2 + 15x - 4x - 60 = 0
(x + 15)(x - 4) = 0
x = - 15, or 4
However, the initial condition is that x must be less than zero. Hence, only one solution from Case 2, i.e. x = - 15

Therefore, from Case 1 & Case 2, we get two solutions of x, i.e. x = - 15, 15. So, number of real solutions for the equation x2 – 11|x| - 60 = 0 is 2.

Hence, the Correct Answer is Option B. 2

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Re: How many real solutions exist for the equation x2 – 11|x| - 60 = 0? 3  [#permalink]

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New post 09 Jan 2020, 05:03
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Re: How many real solutions exist for the equation x2 – 11|x| - 60 = 0? 3   [#permalink] 09 Jan 2020, 05:03
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