Prove-that-to-each-quadratic-factor-in-the-denominator-of-the-form-ax-2-bx-c-which-does-not-have-linear-factors-there-corresponds-to-a-partial-fraction-of-the-form-Ax-B-ax-2-bx-

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Question Number 43705 by Tawa1 last updated on 14/Sep/18

$$\mathrm{Prove}\mathrm{that}\mathrm{to}\mathrm{each}\mathrm{quadratic}\mathrm{factor}\mathrm{in}\mathrm{the}\mathrm{denominator}\mathrm{of}\mathrm{the}\mathrm{form}$$$${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}\mathrm{which}\mathrm{does}\mathrm{not}\mathrm{have}\mathrm{linear}\mathrm{factors},\mathrm{there}\mathrm{corresponds}\mathrm{to}$$$$\mathrm{a}\mathrm{partial}\mathrm{fraction}\mathrm{of}\mathrm{the}\mathrm{form}\frac{\mathrm{Ax}+\mathrm{B}}{{\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}}\mathrm{where}\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{are}\mathrm{constant}.$$

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