Question
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.