Question Number 47301 by myear last updated on 08/Nov/18
$$\mathrm{If}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} +{px}+{q}\:=\mathrm{0}\:\mathrm{has}\:\mathrm{roots} \\ $$$${a}\:\mathrm{and}\:{b}\:\mathrm{where}\:{p},\:{q}\:\mathrm{are}\:\mathrm{non}−\mathrm{zero}\: \\ $$$$\mathrm{constants}.\:\mathrm{Then} \\ $$
Answered by Kunal12588 last updated on 08/Nov/18
$$\left({x}−{a}\right)\left({x}−{b}\right)={x}^{\mathrm{2}} +{px}+{q} \\ $$$${x}^{\mathrm{2}} −\left({a}+{b}\right){x}+{ab}={x}^{\mathrm{2}} +{px}+{q} \\ $$$${comparing}\:{both}\:{sides} \\ $$$$−\left({a}+{b}\right)={p} \\ $$$${ab}={q} \\ $$