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Re: What is the product of all roots of the equation (x
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16 Jan 2018, 07:02
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MathRevolution wrote:
[GMAT math practice question]
What is the product of all roots of the equation \((x+1)^2=|x+1|\)?
\(A. -2\) \(B. -1\) \(C. 0\) \(D. 1\) \(E. 2\)
Hi...
you are required to relook into the OA.. \((x+1)^2=|x+1|\) at the first look will give 0 as a root.. x as 0 will make the equation... \((x+1)^2=|x+1|........(0+1)^2=|0+1|....1=1\) so product of all roots irrespective of other roots will remain ZERO C..
if you want to solve it..
when x+1 is negative.. \((x+1)^2=|x+1|............x^2+2x+1=-x-1......x^2+3x+2=0.......(x+2)(x+1)=0\) roots are -2 and -1
when x+1 is positive.. \((x+1)^2=|x+1|............x^2+2x+1=x+1......x^2+x=0.......x(x+1)=0\) roots are 0 and -1...
Re: What is the product of all roots of the equation (x
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16 Jan 2018, 08:46
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Top Contributor
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MathRevolution wrote:
[GMAT math practice question]
What is the product of all roots of the equation \((x+1)^2=|x+1|\)?
\(A. -2\) \(B. -1\) \(C. 0\) \(D. 1\) \(E. 2\)
There are 3 steps to solving equations involving ABSOLUTE VALUE: 1. Apply the rule that says: If |x| = k, then x = k and/or x = -k 2. Solve the resulting equations 3. Plug solutions into original equation to check for extraneous roots
Given: (x + 1)² = | x + 1| Apply rule to get two equations: (x + 1)² = x + 1 and -(x + 1)² = x + 1
Take: (x + 1)² = x + 1 Expand and simplify left side: x² + 2x + 1 = x + 1 Set this quadratic equation to equal zero: x² + x = 0 Factor to get: x(x + 1) = 0 So, x = 0 and x = -1 are two solutions (aka roots) of the original equation When we test these two solutions, we find that they BOTH work.
IMPORTANT: At this point, we COULD solve -(x + 1)² = x + 1 for x also. HOWEVER, doing so would be a waste of time since the questions asks us to find the PRODUCT of all possible solutions. Since x = 0 is one of the solutions, we can be sure that the product will be 0