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**Ilsa** Given that $\displaystyle 3p(x^2) - 7qx + 3p = 0 $has equal roots

and $\displaystyle p$ and $\displaystyle q$ are positive,

find the ratio $\displaystyle p : q$

and solve the equation.

(I was able to deduce the relation $\displaystyle 49q^2 = 36p$, but how is the ratio further on calculated?

How are the value of $\displaystyle p$ and $\displaystyle q$ deduced in such a way that substituting their values would solve the equation? )

(The answers provided are $\displaystyle 7 : 6 $ and $\displaystyle 1$.)