Question

f(x)=x^3-ax
What values of a guarantee that f(x) will have 3 roots (hint: should be an interval)

Answer 1

I assume 3 real roots here is implied, you'll always get 3 complex ones. :-)
\[x^3-ax=x(x^2-a)=0\]if\[x=0\]or\[x^2-a=0\]\[x^2=a\]\[x=\pm \sqrt{a}\]which thus constrains a to be non-negative or\[a\in [0, \infty]\]

Answer 2

ok thanks that makes sense