Common root of two quadratics (A value α that makes both quadratics zero; subtract suitable multiples)

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A value α that makes both quadratics zero; subtract suitable multiples to get a linear equation in α

What each symbol means

SymbolWhat it stands for
ai,bi,ciCoefficients of the two equations

When to use this

Typically a1,a2 nonzero; degenerate cases need separate check.