Hello,
I am not able to solve this question so can anyone please help me. The question as it is -

Let z1 and z2 be the roots of the equation z^2 + pz + q = 0, where p and q may be complex number. Let A and B represent z1 and z2 in the complex plane. If angle AOB=a not equal to 0 and OA=OB,where O is the origin then p^2 =

- 4qcos^2 (a/2)
- 2qcos^2(a)
- qcos^2 (a/4)

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestAnswer is 1.

\(By\quad rotation\quad ,\\ { z }_{ 1 }={ z }_{ 2 }{ e }^{ ia }\\ From\quad quadratic\quad ,\\ { z }_{ 1 }{ z }_{ 2 }=q\\ Eliminating\quad we\quad get\quad ,\\ { z }_{ 1 }=\sqrt { q } { e }^{ -\cfrac { ia }{ 2 } }\\ { z }_{ 2 }=\sqrt { q } { e }^{ \frac { ia }{ 2 } }\\ Sum\quad of\quad roots\quad is\quad p,\\ Hence\quad ,\\ { p }^{ 2 }=4q\cos ^{ 2 }{ \frac { a }{ 2 } } \)

Log in to reply

Thankyou very much for the solution.

Log in to reply