The function $f$ has the rule $f(x) = px^2 + 4x + q$ for $x \in \mathbb{R}$, where $p$ and $q$ are constants.
(a(i))[3]
Given that $p = 2$ and $q = 10$, write $f(x)$ in the form $a(x+b)^2 + c$, with $a$, $b$ and $c$ constants.
(a(ii))[1]
State the range for $f$.
(b)[5]
Now take $q = -5$, and suppose the roots of $f(x) = 0$ are $5m$ and $-9m$, where $m$ is a constant. Determine $p$ and $m$.
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