double roots help?

Question

Find C such that polynomial function f(x)=4x^3 + Cx - 27 has a double root

Answer 1

If f(x) has a double root this also root of the derivative
f´(x) =12x^2+C=0 so x=+-sqrt(-C/12) so C must be negative
so C=-27 and x= -sqrt(27/12) =-3/2