# For what values of $k$ is $x^2 + 6kx +144$ always positive? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource
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 $k$.