Question

Find the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \).

• A. 2 and 3
• B. 3 and -2
• C. -2 and -3
• D. 1 and 6

Hint:

Remember: To factorize a quadratic equation, find two numbers that multiply to the constant term and add to the coefficient of the linear term.

Answer 1

The Correct Option is A

Given: The quadratic equation is: \[ x^2 - 5x + 6 = 0 \] Step 1: Factorize the quadratic equation We look for two numbers that multiply to \( 6 \) and add up to \( -5 \). These numbers are \( -2 \) and \( -3 \). Thus, we can factorize the quadratic as: \[ (x - 2)(x - 3) = 0 \] Step 2: Solve for \( x \) From the factored form, we have: \[ x - 2 = 0 \quad \Rightarrow \quad x = 2 \] \[ x - 3 = 0 \quad \Rightarrow \quad x = 3 \] Answer: The correct answer is option (1): 2 and 3.