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What are all of the roots of the equation x^3 = 3x^2 2x ?
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05 Apr 2022, 08:45
05 Apr 2022, 08:45
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What are all of the roots of the equation \(x^3 = 3x^2 − 2x\) ?
(A) −3, 1, 2
(B) −2, 1, 3
(C) 0, 1, 2
(D) 0, 1
(E) 1, 2
(A) −3, 1, 2
(B) −2, 1, 3
(C) 0, 1, 2
(D) 0, 1
(E) 1, 2
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Re: What are all of the roots of the equation x^3 = 3x^2 2x ?
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05 Apr 2022, 09:06
05 Apr 2022, 09:06
1
Carcass wrote:
What are all of the roots of the equation \(x^3 = 3x^2 − 2x\) ?
(A) −3, 1, 2
(B) −2, 1, 3
(C) 0, 1, 2
(D) 0, 1
(E) 1, 2
(A) −3, 1, 2
(B) −2, 1, 3
(C) 0, 1, 2
(D) 0, 1
(E) 1, 2
STRATEGY: As with all GRE Multiple Choice questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
In fact, I can immediately see that x = 0 is a solution, since both sides of the equation would evaluate to be 0.
Let's go with that approach
When we plug x = 0 into the equation, we get: 0³ = 3(0)² − 2(0), which simplifies to be: 0 = 0. WORKS!
Since x = 0 is a solution to the given equation, we can eliminate answers choices A, B and E, since they don't list x = 0 as a possible solution.
This leaves us with answer choices C and D.
Both answer choices say that x = 1, which means x = 1 must be a solution. So we won't bother testing that value.
However, choice C says x = 2 is a solution, and choice D says x = 2 isn't a solution, so let's test x = 2
We get: 2³ = 3(2)² − 2(2), which simplifies to be: 8 = 8. WORKS!
Since x = 2 is a solution to the given equation, we can eliminate answer choices D
Answer: C
ALGEBRAIC APPROACH
Given: x³ = 3x² − 2x
Rearrange terms to get: x³ - 3x² + 2x = 0
Factor out x to get: x(x² - 3x + 2) = 0
Factor the expression in the parentheses to get: x(x - 1)(x - 2) = 0
At this point, we can see that the solutions are x = 0, x = 1 and x = 2
Answer: C
gmatclubot
Re: What are all of the roots of the equation x^3 = 3x^2 2x ? [#permalink]
05 Apr 2022, 09:06
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