TS EAMCET · Maths · Complex Number
Let \(a, b \in \mathbf{R}\) and the roots \(\alpha, \beta\) of the equation \(z^2+a z+b=0\) be complex. If the origin, \(\alpha\) and \(\beta\) represent the vertices of an equilateral triangle on the Argand plane, then
- A \(a=b\)
- B \(a^2=3 b\)
- C \(a^2=4 b\)
- D \(a=3 b\)
Answer & Solution
Correct Answer
(B) \(a^2=3 b\)
Step-by-step Solution
Detailed explanation
We have, \(\alpha\) and \(\beta\) are roots of equation \(z^2+a z+b=0\) \(\therefore \alpha+\beta=-a\) and \(\alpha \beta=b\) Now, \(0 < \alpha, \beta\) forms a equilateral triangle…
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