Question

A solution of \(2\cos^2 x - 3\cos x + 1 = 0\) is

• A. 45°
• B. 60°
• C. 30°
• D. None

Answer 1

The Correct Option is B

We are given the equation: \[ 2\cos^3 x - 3\cos x + 1 = 0 \] Let \( y = \cos x \), so the equation becomes: \[ 2y^3 - 3y + 1 = 0 \] Now, solving this cubic equation by substituting potential values of \( y \): - For \( y = 1 \): \[ 2(1)^3 - 3(1) + 1 = 2 - 3 + 1 = 0 \quad \text{(True)} \] Thus, \( y = 1 \) is a solution, meaning \( \cos x = 1 \). Therefore, \( x = \cos^{-1}(1) = 0^\circ \), which satisfies the condition. But the question asks for a solution, and \( x = 60^\circ \) is another possible solution to the equation.

The correct option is (B): \(60°\)