Real and distinct roots of a cubic equation The real values of $a$ for which the equation $x^3-3x+a=0$ has three real and distinct roots is 

Here is a graphical approach. Note that '+ a' shifts the graph up or down.
1) Disregard '+ a'.
2) Graph $ f(x) = x^3 - 3x $
http://www.wolframalpha.com/input/?i=plot%28x%5E3+-+3x%29#
3) from the graph we see that we must find the y values at the local extrema. You did that already getting y = 2 and -2
4) It should be obvious now by inspection that a must be between -2 and 2
Final answer ,
-2 < a < 2
