The polynomial \(p(x)\) is such that

\(p(x)=ax^3+bx^2+cx-5\),

where \(a\), \(b\) and \(c\) are integers.

It is given that \(p'(0)=12\). It is also given that \(p(x)\) has a factor of \(3x-1\) and a remainder of 95 when divided by \(x-2\).

(a) Find the values of \(a\), \(b\) and \(c\).

(b) Show that the equation \(p(x)=0\) has only one real root.