The equation ${x^2} + px + q = 0$, , where $p$ and $q$ are constants, has roots $ - 3$ and $5$.
a) Find the values of $p$ and $q$.
b) Using these values of $p$ and $q$, find the value of the constant $r$ for which the equation ${x^2} + px + q + r = 0$ has equal roots.
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