Question

If the system of equations (in variables \(x, y, z\)): \(x - 2y + tz = 0\), \(3x + 5y + t^2 z = 0\), and \(6x + ty + f(t)z = 0\) has infinitely many solutions (where \(f(t)\) represents a real function), then:

• A. \( y = f(t) \) is strictly increasing
• B. \( y = f(t) \) is strictly decreasing
• C. \( y = f(t) \) is decreasing
• D. \( y = f(t) \) is increasing

Hint:

A quadratic \( ax^2 + bx + c \) is always positive if \( a > 0 \) and \( D > 0 \). This is a very common way to prove that a function is strictly increasing in calculus problems.

Answer 1

The Correct Option is A