WBJEE · Maths · Complex Number
If \(z_1\) and \(z_2\) be two roots of the equation \(z^2+a z+b=0, a^2 \lt 4 b\), then the origin, \(z_1\) and \(z_2\) form an equilateral triangle if
- A \(a^2=3 b^2\)
- B \(a^2=3 b\)
- C \(b^2=3 a\)
- D \(b^2=3 a^2\)
Answer & Solution
Correct Answer
(B) \(a^2=3 b\)
Step-by-step Solution
Detailed explanation
Hint: Here, \(z_1+z_2=-a\) and \(z_1 z_2=b\) \(z_2=z_1 e^{i \pi / 3}=z_1\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right)=z_1\left(\frac{1}{2}+i \cdot \frac{\sqrt{3}}{2}\right)\)…
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