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01 May 2025, 23:31
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A
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Difficulty:
65%
(hard)
Question Stats:
53% (01:36) correct
47%
(01:30)
wrong
based on 260
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If x^2 + 6|x| - 40 = 0, how many real values does x have?
A. 2
B. 4
C. 1
D. 6
E. 8
A. 2
B. 4
C. 1
D. 6
E. 8
01 May 2025, 23:40
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Divyanshu14
If x≥0, |x| = x => x^2 + 6x - 40 = 0
x = -10 or 4
But x ≥ 0 => x = 4
If x<0, |x| = -x => x^2 - 6x - 40 = 0
x = 10 or -4
But x < 0 => x = -4
Ans A
Alt: x^2 = |x|^2
Replacing: |x|^2 + 6|x| - 40 = 0
=> (|x|+10)(|x|-4)=0
=> |x| = 4 or -10
Since |x| cannot be negative, we have
|x| = 4
=> x = ±4
Ans A
06 May 2025, 07:48
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We need to find how many real values does x have if \(x^2 + 6|x| - 40 = 0\)
So, there are two solutions for x = -4, 4
So, Answer will be A
Hope it helps!
Watch the following video to MASTER Absolute Values
| We have two cases as we have |x| | |
| -Case 1: x ≥ 0 => |x| = x => \(x^2 + 6x - 40 = 0\) => \(x^2 + 10x - 4x - 40 = 0\) => x * (x + 10) - 4 * (x + 10) = 0 => (x - 4) * (x + 10) = 0 => x = -10, 4 But the condition was x ≥ 0 => x = 4 is a SOLUTION | -Case 2: x ≤ 0 => |x| = -x => \(x^2 - 6x - 40 = 0\) => \(x^2 - 10x + 4x - 40 = 0\) => x * (x - 10) + 4 * (x - 10) = 0 => (x - 10) * (x + 4) = 0 => x = 10, -4 But the condition was x ≤ 0 => x = -4 is a SOLUTION |
So, there are two solutions for x = -4, 4
So, Answer will be A
Hope it helps!
Watch the following video to MASTER Absolute Values
