JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

The roots of the cubic equation

(z+a b)^3=a^3

, where

a \neq 0

represents the vertices of a triangle. If

\alpha, \beta

and

\gamma

are the roots, then find the value of

|\alpha-\beta|

View answer and explanation

Correct option: D

\sqrt{3}|a b|

Option D (

\sqrt{3}|a b|

) is correct because the roots of the cubic equation represent vertices of an equilateral triangle, and the distance between two vertices is

\sqrt{3}|ab|

More Questions from COMPLEX NUMBERS

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{\left| {1 - i} \right|^x} = {2^x}

|z|=1

z \neq \pm 1

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\left|\sum\limits_{r=1}^n z_r\right|

{z^2} + {\left| z \right|^2} = 0,

z \in C

2x = - 1 + \sqrt 3 i

{\left( {1 - {x^2} + x} \right)^6} - {\left( {1 - x + {x^2}} \right)^6}

\frac{{1 + i\sqrt 3 }}{{\sqrt 3 + i}}