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Question:

 Jul 24, 2021
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Like this

 

\(\lfloor 2x^2-x \rfloor=0\\ \text{It will be true when }\qquad 0\le2x^2-x <1\\~\\ Let\;\;y=2x^2-x\\ \text{It will be true when }\qquad 0\le y<1\\~\\ \)

 

y=2x^2-x \\

y=x(2x-1)

 

this is a concave up parabola with roots of x=0 and x=0.5

So between x=0 and x=0.5 the y value will be negtive so those points are no good.

 

Where does this parabola intersect with y=1?


\(y=1\\ 1=2x^2-x\\ 2x^2-x-1=0\\ \)

I solved using the quadratic equation
\(x=1 \;\;or\;\;-0.5\\~\\ \text{So the statement will be true for }\quad \\~\\ -0.5

 

 

 Jul 24, 2021

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