Let z_1 and z_2 be two roots of the equation z^2+ az+b=0 ,z being complex. Further, assume that the origin, z_1 and z_2 form an equilateral tringle. Then

Question

Accepted Answer

Correct answer: C. (c) If z_1 ,z_2 and z_3 are vertices of an equilateral triangle. Then, z_1^2+z_2^2+z_3^2=z_1z_2+z_2z_3+z_3z_1 Since, origin, z_1 and z_2 are the vertices of an equilateral triangle, then z_1^2+z_2^2=z_1z_2 ⇒(z_1+z_2)^2=3z_1z_2 … … (i ) Again z_1 ,z_2 are the roots of the equation z^2+ az+b=0 Then, z_1+z_2=-a and z_1z_2=b On putting these values in Eq. (i), we get (-a )^2=3b ⇒a^2=3b

$Let z_{1} and z_{2} be two roots of the equation z^{2} + az + b = 0, z being complex. Further, assume that the origin, z_{1} and z_{2} form an equilateral tringle. Then$

Solution

More Complex Numbers PYQs