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Problem Solving (PS) | Re: What is the product of all the roots on the equation (x-2)^2=|x-2|?

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naman90 wrote:

for x<2
the equation becomes: \((x-2)^2 = (2-x)\)
on solving: x=1 or x=2(not possible, since x<2)

for x>2
the equation can be rewritten as: \((x-2)^2 = (x-2)\)
on solving: x=2(not possible, since x>2) or x=3

for x=2
\((2-2)^2 = (2-2)\); which satisfies the equation.
Hence the roots are 1,2,3
product = 6


Hinaman90 andMathRevolution

I have two fundamental disconnect here with the solution, Kindly explain

1.) Any 2nd degree polynomial will have
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