#1247 · Algebra · Quadratics

Common root of two quadratics

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

~12 minProof · checked by AIquadratic equationscommon root

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

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