What are the roots of the polynomial equation x^2 - 5x + 6 = 0?

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Question: What are the roots of the polynomial equation x^2 - 5x + 6 = 0?

Options:

Correct Answer: x = 2, 3

Solution:

Factoring gives (x - 2)(x - 3) = 0. Thus, the roots are x = 2 and x = 3.

What are the roots of the polynomial equation x^2 - 5x + 6 = 0?

What are the roots of the polynomial equation x^2 - 5x + 6 = 0?

Step 1: Start with the polynomial equation x^2 - 5x + 6 = 0.
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 equation using these numbers: (x - 2)(x - 3) = 0.
Step 5: Set each factor equal to zero: x - 2 = 0 and x - 3 = 0.
Step 6: Solve for x in each equation: x = 2 and x = 3.
Step 7: The roots of the polynomial equation are x = 2 and x = 3.

Quadratic Equations – Understanding how to solve quadratic equations using factoring.
Factoring Polynomials – Recognizing how to factor a quadratic polynomial into linear factors.
Finding Roots – Identifying the values of x that satisfy the equation.