This Should Be Simple, Right?

Algebra Level 4

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

\(p(x)\) 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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