#1248 · Algebra · Quadratics

Parameter for linear factors

If the expression $3 x^{2} + 2 P x y + 2 y^{2} + 2 a x - 4 y + 1$ can be resolved into linear factors, prove that $P$ must be one of the roots of the equation $P^{2} + 4 a P + 2 a^{2} + 6 = 0$ .

~15 minProof · checked by AIquadratic equationsdeterminant conditionlinear factors

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. IX. The Theory of Quadratic Equations, Examples IX.c, No. 6

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