Cubic Divisible by Quadratic Sum of Squares

If $a x^{3} + b x^{2} + c x + d$ is divisible by $x^{2} + h^{2}$ , prove that $a d = b c$ .

~12 minProof · checked by AIundetermined coefficientspolynomial divisiondivisibility

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXII. Undetermined Coefficients, Examples XXII.a, No. 10

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