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$\begin{aligned} p(x)&=&51x^2+mx+c \\ q(x)&=&3x^2+bx+a \end{aligned}$

$p(x)$ and $q(x)$ are two quadratic polynomials with integer coefficients such that $p(r)=q(r)=0$. If $r$ is an irrational number, what is $\dfrac{c}{a}$?

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