Questions: Find all x for which f(x)=0.

Transcript text: (c) Find all $x$ for which $f(x)=0$.

Solution

Step 1: Factor the Polynomial

The polynomial $ f(x) = x^2 - 5x + 6 $ is factorized as follows: \[ f(x) = (x - 3)(x - 2) \]

Step 2: Set the Factors to Zero

To find the values of $ x $ for which $ f(x) = 0 $, we set each factor equal to zero: \[ x - 3 = 0 \quad \text{and} \quad x - 2 = 0 \]

Step 3: Solve for $ x $

Solving the equations from Step 2 gives: \[ x = 3 \quad \text{and} \quad x = 2 \]

Step 4: List the Solutions

The values of $ x $ for which $ f(x) = 0 $ are: \[ x = 2, \quad x = 3 \]

The values of $ x $ for which $ f(x) = 0 $ are $ \boxed{2} $ and $ \boxed{3} $.

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