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

Solution

1. Start with the given quadratic equation: $x^2-5x+6=0$.
2. Find two numbers that multiply to $6$ and add to $-5$, which are $-2$ and $-3$.
3. Rewrite the equation in factored form: $(x-2)(x-3)=0$.
4. Set each factor equal to zero to solve for $x$: $x-2=0$ or $x-3=0$.
5. Solve the equations to find the roots: $x=2$ and $x=3$.
6. Hence the answer is (A).