Question Number 109485 by ZiYangLee last updated on 24/Aug/20
$$\mathrm{If}\:{f}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c},\:{g}\left({x}\right)=\:−{ax}^{\mathrm{2}} +{bx}+{c} \\ $$$$\mathrm{where}\:{ac}\:\neq\:\mathrm{0},\:\mathrm{then}\:{f}\left({x}\right){g}\left({x}\right)=\mathrm{0}\:\mathrm{has} \\ $$
Answered by ajfour last updated on 24/Aug/20
$${f}\left({x}\right){g}\left({x}\right)={h}\left({x}\right)=\left({bx}+{c}\right)^{\mathrm{2}} −{a}^{\mathrm{2}} {x}^{\mathrm{4}} \\ $$$${has}\:{no}\:{real}\:{roots},\:{one}\:{real}\:{root}\:{or} \\ $$$${two}\:{real}\:{roots},\:{not}\:{more}. \\ $$
Commented by ZiYangLee last updated on 24/Aug/20
$$\mathrm{thanks} \\ $$