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: Factorization
Identify two numbers that multiply to \( 6 \) and sum to \( -5 \). These numbers are \( -2 \) and \( -3 \).
The factored form is:
\[ (x - 2)(x - 3) = 0 \]
Step 2: Solution for \( x \)
From the factorization:
\[ x - 2 = 0 \quad \Rightarrow \quad x = 2 \]
\[ x - 3 = 0 \quad \Rightarrow \quad x = 3 \]
Answer: The solutions are \( x=2 \) and \( x=3 \).