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Diffstat (limited to 'execsumm/document.tex')
| -rw-r--r-- | execsumm/document.tex | 10 |
1 files changed, 6 insertions, 4 deletions
diff --git a/execsumm/document.tex b/execsumm/document.tex index 32d4a0a..c308d05 100644 --- a/execsumm/document.tex +++ b/execsumm/document.tex @@ -22,12 +22,14 @@ $$\x' = $$ The characteristic polynomial is $$-\lambda( (-\lambda-C_2(R_1+\rload))(-\lambda-C_1\rload) -+ C_2^2R_1\rload).$$ ++ C_2C_1R_1\rload).$$ Expanded, $$-\lambda( \lambda^2 + \lambda(C_2(R_1+\rload)+C_1\rload) -+ C_1C_2\rload(R_1+\rload) + C_2^2R_1\rload).$$ -In terms of its roots, -$$???$$ ++ C_1C_2\rload(2R_1+\rload)).$$ +In terms of its roots (with $b=C_2(R_1+\rload)+C_1\rload$ and +$c = C_1C_2\rload(2R_1+\rload),$ +$$-\lambda{(\lambda-{-b+\sqrt{b^2-4c}\over2}) +(\lambda-{-b-\sqrt{b^2-4c}\over 2})}$$ \def\bu{\par\leavevmode\llap{\hbox to \parindent{\hfil $\bullet$ \hfil}}} \opt{.15fil} |