Question Number 125131 by Snail last updated on 03/Jun/21
$${Let}\:{a},{b},{c}\in\:{complex}\:{numbers}\:{such}\:{that}\:{the}\:{roots} \\ $$$${of}\:{the}\:{equation}\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0}\:{have}\:{same}\:{modulus} \\ $$$${Prove}\:{that}\:{a}=\mathrm{0}\:{iff}\:{b}=\mathrm{0} \\ $$