Question

If \( (x - 1) \) is a factor of \( 2x^2 - 5x + k = 0 \), then the value of \( k \) is:

• A. 2
• B. 5
• C. 3
• D. 4

Hint:

Use the factor theorem to find unknown coefficients by substituting the root of the factor into the equation.

Answer 1

The Correct Option is C

Step 1: Use the factor theorem.
The factor theorem states that if \( (x - 1) \) is a factor of the polynomial \( 2x^2 - 5x + k \), then substituting \( x = 1 \) into the polynomial should give 0. Substituting \( x = 1 \) into the equation \( 2x^2 - 5x + k = 0 \): \[ 2(1)^2 - 5(1) + k = 0 \] \[ 2 - 5 + k = 0 \] \[ k - 3 = 0 \] \[ k = 3 \] Thus, the value of \( k \) is 3. Therefore, the correct answer is 3. 3.