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

Question: Solve the quadratic equation:

$$x^2-5x+6=0$$

Answer: 

2 or 3

Additional Information :

We are given the quadratic equation:

$$x^2 - 5x + 6 = 0$$

Step 1: Factorize the Equation

We need to find two numbers that multiply to 6 and add to -5.

The numbers -2 and -3 satisfy this condition because:

$$(-2) \times (-3) = 6$$ $$(-2) + (-3) = -5$$

So, we factorize the equation:

$$(x - 2)(x - 3) = 0$$

Step 2: Solve for $x$

Setting each factor to zero:

$$x - 2 = 0 \quad \text{or} \quad x - 3 = 0$$ $$x = 2 \quad \text{or} \quad x = 3$$

Final Answer:

$$\boxed{{\displaystyle x=2,x=3}}$$

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