Let z_1,z_2 be the roots of the equation z^2+az+12=0 and z_1,z_2 form an equilateral trian…

Question

Let $z_1,z_2$ be the roots of the equation $z^2+az+12=0$ and $z_1,z_2$ form an equilateral triangle with the origin. Then the value of $|a|$ is

Answer: 6

Accepted Answer

$z_1+z_2=-a$, $z_1z_2=12$. For $0,z_1,z_2$ equilateral: $z_1^2+z_2^2=z_1z_2$, so $(z_1+z_2)^2=3z_1z_2 \implies a^2=3(12)=36 \implies |a|=6.$

Solutions · 1