Find sup S and inf S, and give reasons for your answers:
S=$$\left\{ x \in \mathbb{R}:2x ^{2}-3x-1

Question

Find sup S and inf S, and give reasons for your answers:
S=$$\left\{ x \in \mathbb{R}:2x ^{2}-3x-1<0 \right\}$$

experimentx · Answer

this is a parabola facing upwards http://www.wolframalpha.com/input/?i=plot+2x^2%E2%88%923x%E2%88%921%3C+0 so the supremum or upper bond will be 0 and the infimum will be at vertex which is at the lower bound.

anonymous · Answer

Wouldn't that gives us values of y though? I was working through it and found the roots, the upper root being the supremum of S and the lower root (the negative one) being the infimum of S.

experimentx · Answer

woops sorry ... it's x right, the two zeros will be the upper and lower bound.

experimentx · Answer

http://www.wolframalpha.com/input/?i=2x%5E2%E2%88%923x%E2%88%921+%3D+0

anonymous · Answer

Awesome, thanks heaps! So just to clarify, if the question started with $$\left\{ y \in \mathbb{R} : y=...<0\right\}$$, we would have the supremum as 0 and the infimum at the vertex y=...

experimentx · Answer

yep ... !!

anonymous · Answer

Thanks!