Which of the following is a root of the polynomial P(x) = x^2 - 5x + 6?

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Question: Which of the following is a root of the polynomial P(x) = x^2 - 5x + 6?

Options:

Correct Answer: 2

Solution:

The roots of the polynomial can be found by factoring it as (x-2)(x-3) = 0, giving roots 2 and 3.

Which of the following is a root of the polynomial P(x) = x^2 - 5x + 6?

Which of the following is a root of the polynomial P(x) = x^2 - 5x + 6?

Step 1: Write down the polynomial P(x) = x^2 - 5x + 6.
Step 2: Look for two numbers that multiply to 6 (the constant term) and add up to -5 (the coefficient of x).
Step 3: The numbers that work are -2 and -3 because -2 * -3 = 6 and -2 + -3 = -5.
Step 4: Rewrite the polynomial using these numbers: P(x) = (x - 2)(x - 3).
Step 5: Set the factored form equal to zero: (x - 2)(x - 3) = 0.
Step 6: Solve for x by setting each factor to zero: x - 2 = 0 or x - 3 = 0.
Step 7: This gives the solutions: x = 2 and x = 3.
Step 8: Therefore, the roots of the polynomial are 2 and 3.

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