Given two functions \( f(x) = x^2 - 3x + 2 \) and \( g(x) = -x^2 + 5x - 6 \). Find the roots of the function \( h(x) = f(x) - g(x) \).

Step 1 ：Step 1: First, we need to find the expression for \( h(x) = f(x) - g(x) \). This is done by subtracting the function \( g(x) \) from \( f(x) \). So, \( h(x) = (x^2 - 3x + 2) - (-x^2 + 5x - 6) \).

Step 2 ：Step 2: Simplify \( h(x) \) to get \( h(x) = 2x^2 - 8x + 8 \).

Step 3 ：Step 3: To find the roots of \( h(x) \), we need to solve the equation \( h(x) = 0 \), i.e., \( 2x^2 - 8x + 8 = 0 \).

Step 4 ：Step 4: Divide every term by 2 to simplify the equation. We get \( x^2 - 4x + 4 = 0 \).

Step 5 ：Step 5: This is a perfect square trinomial. So, \( (x-2)^2 = 0 \).

Step 6 ：Step 6: Solve for \( x \) to get the roots of the equation.