Consider the following for the next items that follow:

Consider equation-I : z3 + 2z2 + 2z + 1 = 0 and equation-II : z1985 + z100 + 1 = 0.

What are the roots of equation-I ?

Consider the following for the next items that follow:

Consider equation-I : z3 + 2z2 + 2z + 1 = 0 and equation-II : z1985 + z100 + 1 = 0.

Which one of the following is a root of equation-II?

Consider the following for the next items that follow:

Consider equation-I : z3 + 2z2 + 2z + 1 = 0 and equation-II : z1985 + z100 + 1 = 0.

What is the number of common roots of equation-I and equation-II?

Consider the following for the next items that follow:

A quadratic equation is given by (a + b) x2 - (a + b + c) x + k = 0, where a, b, c are real.

If $\rm {k}=\frac{{c}}{2},({c} \neq 0)$, then the roots of the equation are :