Question Number 35533 by jonesme last updated on 20/May/18
$$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} −{px}+{q}=\mathrm{0} \\ $$$$\mathrm{differ}\:\mathrm{by}\:\mathrm{unity},\:\mathrm{then} \\ $$
Answered by ajfour last updated on 20/May/18
$$\left(\alpha−\beta\right)^{\mathrm{2}} ={p}^{\mathrm{2}} −\mathrm{4}{q}=\mathrm{1} \\ $$$${or}\:\:\:\:\:{p}^{\mathrm{2}} −\mathrm{4}{q}−\mathrm{1}=\mathrm{0}\:. \\ $$