Timeline for Smallest root of a degree 3 polynomial
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 16 at 5:32 | comment | added | GH from MO | @RiverLi I added a simple proof that (1) has three real roots. See my response below. | |
| Sep 16 at 1:48 | comment | added | River Li | @Venus My proof for $g(a,b,c)\ge 0$ for all reals is complicated. Actually I hope to see a simple proof for the statement that (1) has three real roots. | |
| Sep 16 at 1:40 | comment | added | Venus | @RiverLi Then could the computer or could you have the computer show the steps? Thanks. | |
| Sep 16 at 1:30 | comment | added | River Li | @Venus When $r < 0$, then $f(0) > 0$ and there is a negative root. Can you find them such that $r < 0$? | |
| Sep 16 at 1:20 | comment | added | River Li | @Venus I think proof is referred to as a human verifiable proof of the inequalities (sometimes we use computer to motivate the proof, but the proof itself is verifiable by hand usually), while verification is to use computer to verify the inequalities without showing the steps. | |
| Sep 16 at 1:10 | comment | added | Venus | Thank you for your answer. Are verification and proof the same? Since you said that you "can prove that $g(a, b, c) \ge 0$ for all real numbers $a, b, c$," could you please show the proof? Thanks. | |
| Sep 15 at 23:37 | history | edited | River Li | CC BY-SA 4.0 |
change notation
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| Sep 15 at 23:35 | comment | added | River Li | @GHfromMO Thanks. I will edit. | |
| Sep 15 at 16:35 | comment | added | GH from MO | It is confusing to write $f(a,b,c)$ when you already use the notation $f(s)$. | |
| Sep 15 at 15:35 | history | edited | River Li | CC BY-SA 4.0 |
added 782 characters in body
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| Sep 15 at 14:50 | history | edited | River Li | CC BY-SA 4.0 |
added 82 characters in body
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| Sep 15 at 14:45 | history | answered | River Li | CC BY-SA 4.0 |