Quadratic Equations

We have, and let Let and Further, let and be the affixes of points A and B respectively. Then, and is an equilateral triangle. Thus, .

Given that tan A and tan B are the roots of Now, Now,

Given equation is Roots of the equation are and . and

Step 1: Find Given: Differentiate both sides: Substituting : Step 2: Find Differentiating again: So: Step 3: Compute Thus, the correct answer is (C) 2.

Step 1: Analyze the given equations.
We are given two equations: and We can substitute into the first equation.
Step 2: Solve for .
Substitute into the first equation: Simplifying the equation: Now, assume that and (as a possible approach), then substitute into the equation:
Final Answer: 160.