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Question: The common roots of the equation z<sup>3</sup> + 2z<sup>2</sup> + 2z + 1 = 0 and z<sup>1985</sup> +...

The common roots of the equation

z3 + 2z2 + 2z + 1 = 0 and z1985 + z100 + 1 = 0 are –

A

– 1 ,w

B

– 1 , w2

C

w, w2

D

w, – w2

Answer

w, w2

Explanation

Solution

Sol. (z + 1) (z2 + z + 1) = 0 Ž z = – 1, w, w2

As – 1 does not satisfy z1985 + z100 + 1 = 0

So, w, w2 are the common roots.