JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(z_{1}, z_{2}\) be the roots of the equation \(z^{2}+a z+\) \(12=0\) and \(z _{1}, z _{2}\) form an equilateral triangle with origin. Then, the value of \(| a |\) is
- A \(4\)
- B \(6\)
- C \(12\)
- D \(3\)
Answer & Solution
Correct Answer
(B) \(6\)
Step-by-step Solution
Detailed explanation
If \(0, z , z _{2}\) are vertices of equilateral triangles \(\Rightarrow 0^{2}+z_{1}^{2}+z_{2}^{2}=0\left(z_{1}+z_{2}\right)+z_{1} z_{2}\) \(\Rightarrow\left(z_{1}+z_{2}\right)^{2}=3 z_{1} z_{2}\) \(\Rightarrow a ^{2}=3 \times 12\) \(| a | =6\)
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