Quintic Divisible by a Squared Linear Factor

If $x^{5} - 5 q x + 4 r$ is divisible by $(x - c)^{2}$ , shew that $q^{5} = r^{4}$ .

~15 minProof · checked by AIundetermined coefficientsdivisibilityderivative test

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXII. Undetermined Coefficients, Examples XXII.a, No. 11

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