If a polynomial p(x) is given by p(x) = x^2 - 5x + 6, what are the roots of the

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Question: If a polynomial p(x) is given by p(x) = x^2 - 5x + 6, what are the roots of the polynomial?

Options:

Correct Answer: 2 and 3

Solution:

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

If a polynomial p(x) is given by p(x) = x^2 - 5x + 6, what are the roots of the polynomial?

If a polynomial p(x) is given by p(x) = x^2 - 5x + 6, what are the roots of the polynomial?

Step 1: Write down the polynomial p(x) = x^2 - 5x + 6.
Step 2: Look for two numbers that multiply to the constant term (6) and add up to the coefficient of x (-5).
Step 3: The two 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.

Factoring Polynomials – The process of expressing a polynomial as a product of its factors to find its roots.
Finding Roots – Identifying the values of x for which the polynomial equals zero.