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-

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

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

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