The expression \[2x^4+ax^3+bx^2-4x-4\] where \(a\) and \(b\) are constants, is denoted by \(f(x)\). Given that \(f\left(-\dfrac{1}{2}\right)=0\) and \(f(2)=0\), find the values of \(a\) and \(b\).
With these values for \(a\) and \(b\)
express \(f(x)\) as the product of three algebraic factors, and hence show that the equation \(f(x)=0\) has only two real roots;
find the set of values of \(x\) for which \(f(x)>0\).
