Common root of two quadratics

If the equations $x^2+px+q=0$ and $x^2+p^{\prime }x+q^{\prime }=0$ have a common root, shew that it must be either $\frac{p{q}^{\prime }-p^{\prime }q}{q-q^{\prime }}$ or $\frac{q-q^{\prime }}{p^{\prime }-p}$.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. IX. The Theory of Quadratic Equations, Examples IX.c, No. 4