Question
Question: Let z<sub>1</sub> and z<sub>2</sub> be the non-real roots of the equation 3z<sup>2</sup> + 3z + b = ...
Let z1 and z2 be the non-real roots of the equation 3z2 + 3z + b = 0. If the origin together with the points represented by z1 and z2 form an equilateral triangle then the value of b is–
A
1
B
2
C
3
D
None of these
Answer
1
Explanation
Solution
Sol. z1 + z2 = –1 and z1z2 = b/3
z2 and origin form an equilateral triangle
z12 + z22 + z32 = z1z2 + z2z3 + z3z1
Ž (z1 + z2)2 = 3 z1z2 Ž b = 1