If f(x) = x^2 - 6x + 8, what are the roots of f(x)?

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Question: If f(x) = x^2 - 6x + 8, what are the roots of f(x)?

Options:

Correct Answer: 2 and 4

Solution:

Factoring gives f(x) = (x - 2)(x - 4). Setting each factor to zero gives the roots x = 2 and x = 4.

If f(x) = x^2 - 6x + 8, what are the roots of f(x)?

If f(x) = x^2 - 6x + 8, what are the roots of f(x)?

Step 1: Start with the function f(x) = x^2 - 6x + 8.
Step 2: We need to factor the quadratic expression x^2 - 6x + 8.
Step 3: Look for two numbers that multiply to +8 (the constant term) and add to -6 (the coefficient of x).
Step 4: The numbers -2 and -4 work because -2 * -4 = 8 and -2 + -4 = -6.
Step 5: Rewrite the quadratic as f(x) = (x - 2)(x - 4).
Step 6: To find the roots, set each factor equal to zero: x - 2 = 0 and x - 4 = 0.
Step 7: Solve for x in each equation: from x - 2 = 0, we get x = 2; from x - 4 = 0, we get x = 4.
Step 8: The roots of f(x) are x = 2 and x = 4.

Quadratic Functions – Understanding how to find the roots of a quadratic function through factoring.
Factoring – The process of rewriting a quadratic expression as a product of its linear factors.
Zero Product Property – The principle that if the product of two factors is zero, at least one of the factors must be zero.