both of the following cubics have an inflection point at
do either have a root at ?
I've been studying methods for finding the roots of cubic functions. The general formulae seem overwhelmingly difficult to remember. I know it customary for students to memorize the quadratic formula, but what about the formula seen here: Cubic Formula -- from Wolfram MathWorld
?
LOL, how could anybody possilby do something like that on a test? The cubic formula seems impossible to remember, so I just made up a different method. Say I have a cubic equation .
If you look at the graphs of cubic functions, there always seems to be a point of inflection at the x-intercept. Is this true in general? If so, then gives the root , So now I proceed with synthetic division. Is this method something I can rely on? Are there always roots at the inflection points of cubic functions?
Generally,
Notice that
I'm not good at proving things in math, so I don't know if I can claim that this works in general, and that all cubic functions will have at least one root of the form
ok, so my method works mererly as a test. Set f''(x)=0, maybe you'll find a root. The is easy to solve by factoring, so this one wouldn't be a problem. Other cubic function are more difficult to deal with, so I'm trying to explore simplified methods of finding the roots.