Dichotomy method using BC

#!/bin/bash
#Dichotomy method
#Equalation acoef*x^2+bcoef*x
acoef="0.5"
bcoef="2"
#[a;b]
a="-2"
b="-3"
#Epsilon, accuracy
e="10^-6"

#BC returnes 1 if true and 0 if false
#BC has no ABS function by default
statement=$(echo "define abs(x) {if (x<0) {return -x}; return x;};  abs($b - $a) > $e" | bc)
# [[ works only in bash shell, newer ]]
# [ works in default shell ]
while [[ $statement = 1 ]]
do
#scale makes 6 digits after comma
c=$(echo "scale=6; ($a + $b) / 2" | bc)
        statement=$(echo "scale=6; ($b * $b * $acoef + $b * $bcoef) * ($c * $c * $acoef + $c * $bcoef) < 0" | bc)
        if [[ $statement = 1 ]]
                then
                        a=$c
                else
                        b=$c
        fi
statement=$(echo "define abs(x) {if (x<0) {return -x}; return x;};  abs($b - $a) > $e" | bc)
done
echo "scale=6; ($a + $b) / 2" | bc

exit 0