Solve the equation x² − 5x + 6 = 0

Answer: \(\boxed{x=2 \text{ or } x=3}\)

Factor the quadratic:

\[ x^2-5x+6=(x-2)(x-3) \]

because \((-2)(-3)=6\) and \(-2+(-3)=-5\).

Now use the zero-product rule:

\[ (x-2)(x-3)=0 \]

So one of the factors must equal zero:

\[ x-2=0 \Rightarrow x=2 \]

\[ x-3=0 \Rightarrow x=3 \]

Check:

• \(2^2-5\cdot2+6=4-10+6=0\)
• \(3^2-5\cdot3+6=9-15+6=0\)

Both solutions are correct.