Let $z_{1}$ and $z_{2}$ be two imaginary roots of $z^{2}+p z+q=0$ , where $p$ and $q$ are real. The points $z_{1}, z_{2}$ and origin form an equilateral triangle if

Question

Let $z_{1}$ and $z_{2}$ be two imaginary roots of $z^{2}+p z+q=0$ , where $p$ and $q$ are real. The points $z_{1}, z_{2}$ and origin form an equilateral triangle if

2 Answers

kritika · Answer 1 · 2021-12-26T19:26:53+0000

Ans: (C)
Hint:

$\mathrm{O}^{2}+\mathrm{z}_{1}{ }^{2}+\mathrm{z}_{2}{ }^{2}=\mathrm{z}_{1} \mathrm{z}_{2}$

$\begin{aligned} &\Rightarrow z_{1}{ }^{2}+z_{2}{ }^{2}=z_{1} z_{2} \\ &\Rightarrow\left(z_{1}+z_{2}\right)^{2}=3 z_{1} z_{2} \\ &\Rightarrow p^{2}=3 q \end{aligned}$

Let $z_{1}$ and $z_{2}$ be two imaginary roots of $z^{2}+p z+q=0$ , where $p$ and $q$ are real. The points $z_{1}, z_{2}$ and origin form an equilateral triangle if

Your answer

2 Answers

Your comment on this answer:

Your comment on this answer:

Related questions

Categories

Let z1z_{1} and z2z_{2} be two imaginary roots of z2+pz+q=0z^{2}+p z+q=0, where pp and qq are real. The points z1,z2z_{1}, z_{2} and origin form an equilateral triangle if

Your answer

2 Answers

Your comment on this answer: