If and are the cube roots of ( )

MATHEMATICS · Single correct · ISC · Mathematics · Algebra · Algebra

Problem

\alpha, \beta

and

\gamma

are the cube roots of

p

(

p < 0

), then for any

x, y

and

z

\frac{x\alpha + y\beta + z\gamma}{x\beta + y\gamma + z\alpha}

is equal to (1)

\frac{1}{2}(-1 - i\sqrt{3}), i = \sqrt{-1}

(2)

\frac{1}{2}(1 + i\sqrt{3}), i = \sqrt{-1}

(3)

\frac{1}{2}(1 - i\sqrt{3}), i = \sqrt{-1}

(4) None of these