Question
The solutions to the equation f(x) = x2 − 5x + 6 when f(x) = 0
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GPT-4o mini
To find the solutions to the equation \( f(x) = x^2 - 5x + 6 \) when \( f(x) = 0 \), we need to solve the quadratic equation \( x^2 - 5x + 6 = 0 \).
We can factor the quadratic as follows:
\[
x^2 - 5x + 6 = (x - 2)(x - 3) = 0
\]
Now, we set each factor equal to zero:
1. \( x - 2 = 0 \) ⟹ \( x = 2 \)
2. \( x - 3 = 0 \) ⟹ \( x = 3 \)
Therefore, the solutions to the equation \( f(x) = 0 \) are:
\[
x = 2 \quad \text{and} \quad x = 3
\]
We can factor the quadratic as follows:
\[
x^2 - 5x + 6 = (x - 2)(x - 3) = 0
\]
Now, we set each factor equal to zero:
1. \( x - 2 = 0 \) ⟹ \( x = 2 \)
2. \( x - 3 = 0 \) ⟹ \( x = 3 \)
Therefore, the solutions to the equation \( f(x) = 0 \) are:
\[
x = 2 \quad \text{and} \quad x = 3
\]
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