added quadratic formula solution

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}