Question

Solve the quadratic equation: \[ x^2 - 5x + 6 = 0 \]

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

Hint:

To solve a quadratic equation, look for two numbers that multiply to the constant term and add up to the coefficient of the middle term.

Answer 1

The Correct Option is C

Step 1: Write the given quadratic equation. The quadratic equation is: \[ x^2 - 5x + 6 = 0 \] Step 2: Factorize the quadratic equation. We need to factorize \( x^2 - 5x + 6 \). We look for two numbers that multiply to give \( 6 \) and add up to \( -5 \). These numbers are \( -2 \) and \( -3 \). Thus, the factorized form is: \[ (x - 2)(x - 3) = 0 \] Step 3: Solve for \( x \). Set each factor equal to zero: \[ x - 2 = 0 \quad \text{or} \quad x - 3 = 0 \] \[ x = 2 \quad \text{or} \quad x = 3 \] Answer: Therefore, the solutions are \( x = 2 \) and \( x = 3 \).