From f367c3918b1f068db4032a67bd489315719f2e9e Mon Sep 17 00:00:00 2001 From: Holden Rohrer Date: Tue, 14 Apr 2020 12:18:22 -0400 Subject: added quadratic formula solution --- execsumm/document.tex | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) (limited to 'execsumm') 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} -- cgit