Question

If \( x^2 - 5x + 6 = 0 \), what are the possible values of \( x \)? 

• A. \( x = 1 \) or \( x = 6 \)
• B. \( x = 2 \) or \( x = 3 \)
• C. \( x = -2 \) or \( x = -3 \)
• D. \( x = -1 \) or \( x = 6 \)

Hint:

To solve quadratic equations, try factoring first to find roots quickly.

Answer 1

The Correct Option is B

Factor the quadratic equation by finding two numbers that multiply to give the constant term and add to give the coefficient of the linear term: \[ (x - 2)(x - 3) = 0. \] Set each factor equal to zero: \[ x - 2 = 0
\Rightarrow
x = 2, \] \[ x - 3 = 0
\Rightarrow
x = 3. \] Therefore, \[ x = 2
\text{or}
x = 3. \]