Question

`z_1a n dz_2` are the roots of `3z^2+3z+b=0.` if `O(0),(z_1),(z_2)` form an equilateral triangle, then find the value of `bdot`

Answer 1

Here, `z_(1)+z_(2)=-1,z_(1)z_(2)=(b)/(3)`
Triangle OAB is equilateral. So,
`0^(2)+z_(1)^(2)+z_(2)^(2)=0xxz_(1)+0xxz_(2)+z_(1)z_(2)`
or `(z_(1)+z_(2))^(2)-2z_(1)z_(2)=z_(1)z_(2)`
or `1=3z_(1)z_(2)=3(b)/(3)`
or `b=1`