Consider the following for the next two (02) items that follow:
Let \( Z_{1} \) and \( Z_{2} \) be any two complex numbers such that \( Z_{1}^{2} + Z_{2}^{2} + Z_{1}Z_{2} = 0 \).
What is the value of \( \left|\frac{Z_{1}}{Z_{2}}\right| \)?
Consider the following for the next two (02) items that follow:
The product of five consecutive terms of an AP is 229635. The first, second and fifth terms are in GP.
Consider the following for the next two (02) items that follow:
Let \( (8 + 3\sqrt{7})^{20} = U + V \) and \( (8 - 3\sqrt{7})^{20} = W \), where U is an integer and 0 < V < 1.
Consider the following for the next two (02) items that follow:
The roots of the quadratic equation \( a^{2}(b^{2} - c^{2})x^{2} + b^{2}(c^{2} - a^{2})x + c^{2}(a^{2} - b^{2}) = 0 \) are equal \( (a^{2} \neq b^{2} \neq c^{2}) \).
Which one of the following statements is correct?
A.
\( a^{2}, b^{2}, c^{2} \) are in AP.
B.
\( a^{2}, b^{2}, c^{2} \) are in GP.
C.
\( a^{2}, b^{2}, c^{2} \) are in HP.
D.
\( a^{2}, b^{2}, c^{2} \) are neither in AP nor in GP nor in HP.
