Find the roots of the polynomial equation x^2 + 5x + 6 = 0.

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Question: Find 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.

Find the roots of the polynomial equation x^2 + 5x + 6 = 0.

Find 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 2 and 3 work 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 are x = -2 and x = -3.

Factoring Quadratic Equations – The process of expressing a quadratic polynomial as a product of its linear factors to find its roots.
Quadratic Formula – An alternative method to find roots of a quadratic equation, applicable when factoring is not straightforward.