Question

What is the other root of \(f(x) = 0\)?

• A. \(-7\)
• B. \(-4\)
• C. \(2\)
• D. \(6\)
• E. cannot be determined

Hint:

When one root is known, factorize and use given functional values to find the other root.

Answer 1

The Correct Option is D

Given \(3\) is a root, \(f(x)\) can be written as: \[ f(x) = a(x - 3)(x - r) \] where \(r\) is the other root. From \(f(5) = -3f(2)\): \[ a(5 - 3)(5 - r) = -3a(2 - 3)(2 - r) \] \[ 2(5 - r) = -3(-1)(2 - r) \] \[ 2(5 - r) = 3(2 - r) \] \[ 10 - 2r = 6 - 3r \] \[ r = 6 \] Thus, the other root is \(\boxed{6}\).