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555-605 (Medium)|   Algebra|      
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If r^3 + |r| = 0, what are the sum of all possible values of r? 07 Jan 2021, 10:21
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B
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35% (medium)

Question Stats:

59% (01:05) correct 41% (01:17) wrong based on 202 sessions

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If r^3 + |r| = 0, what are the sum of all possible values of r?

A. -2
B. -1
C. 0
D. 1
E. 2
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B
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If r^3 + |r| = 0, what are the sum of all possible values of r? 07 Jan 2021, 10:32
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If r^3 + |r| = 0, what are the sum of all possible values of r?

Since |r| can be only positive or 0, r^3 can either be 0 or -1

So the sum is 0 + (-1) = -1

Answer Option B
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If r^3 + |r| = 0, what are the sum of all possible values of r? 08 Jan 2021, 02:07
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r^3 + |r| = 0 is only possible for two values of r: 0 and -1

=> 0^3 + |0| = 0

=> (-1)^3 + |(-1)| = -1 + 1 = 0

Therefore, 0 + (-1) = -1

Answer B
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If r^3 + |r| = 0, what are the sum of all possible values of r? 20 Sep 2022, 09:54
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Given that r^3 + |r| = 0 and we need to find the sum of all possible values of r

Theory:

    ⁍➡ |A| = A if A ≥ 0
    ⁍➡ |A| = -A if A < 0


Case 1: r ≥ 0

|r| = r
=> r^3 + r = 0
=> r*(r^2 + 1) = 0
=> r = 0 or r^ = -1
ONLY real solution is r = 0

Case 2: r < 0

|r| = -r
=> r^3 - r = 0
=> r*(r^2 - 1) = 0
=> r*(r + 1)*(r - 1) = 0
=> r = 0 or r = 1 or r = -1
But condition was r < 0
=> Solution is r = -1

=> Solution is r = 0 and r = -1

Sum of all the values = 0 + -1 = -1

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Absolute Values

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If r^3 + |r| = 0, what are the sum of all possible values of r? 10 Feb 2026, 03:39
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Deconstructing the Question
Solve:
\(r^3 + |r| = 0\)
and find the sum of all real solutions.

Step-by-step
Case 1: \(r \ge 0\) so \(|r| = r\)
\(r^3 + r = 0\)
\(r(r^2+1)=0\)
Real solution: \(r=0\)

Case 2: \(r < 0\) so \(|r| = -r\)
\(r^3 - r = 0\)
\(r(r^2-1)=0\)
\(r(r-1)(r+1)=0\)
With \(r<0\), valid solution: \(r=-1\)

Solutions: \(r=0,\,-1\)
Sum:
\(0 + (-1) = -1\)

Answer: -1 (B)
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