; General quadratic (2nd degree polynomial) formula.
; Formula for the 2 roots (solutions for x)
; of the general quadratic equation.
;
a x^2 + b x + c = 0 ; The general quadratic equation.
copy select ; Make a copy and select it.
solve verifiable for x ; Mathomatic can easily solve and verify that:
; This is the quadratic formula.
; The coefficients (a, b, and c) may be any mathematical expression not containing x.
pause
; Here is the derivation and proof of the quadratic formula,
; without actually using the quadratic formula,
; because that is what we are trying to derive now, from the quadratic equation:
#1:
copy select ; make a copy of the general quadratic equation to work on and select it.
-=c ; subtract "c" from both sides.
/=a ; divide both sides by "a".
pause Next simplify it and turn it into a repeated factor polynomial equation
simplify
+=b^2/(4*(a^2)) ; add "b^2/(4*(a^2))" to both sides.
; Now the LHS is a repeated factor polynomial, next factor it by pressing Enter to simplify.
pause
simplify ; Now the LHS is a factored polynomial, so solving for the single "x" is easy.
set debug 1 ; Let Mathomatic do the work and show it too.
; Show how easy it is to solve this equation now, after pressing Enter.
pause
x
; Here is the raw solve result, press the Enter key to simplify and compare with the quadratic formula.
pause
set no debug
repeat simplify
compare with 2