Question

Write \(x^2 + 6kx +144\) in the form \((x+p)^2+q\) and thus obtain expressions for \(p\) and \(q\) in terms of \(k\). Hence find the range of values for \(k^2\) such that \(x^2+6kx+144\) is positive for all values of \(x\), and deduce the corresponding range of values of \(k\).