Determine the product of the roots of the equation x² + 6x + 9 = 0. (2021)

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Question: Determine the product of the roots of the equation x² + 6x + 9 = 0. (2021)

Options:

Correct Answer: 9

Solution:

The product of the roots is c/a = 9/1 = 9.

Determine the product of the roots of the equation x² + 6x + 9 = 0. (2021)

Determine the product of the roots of the equation x² + 6x + 9 = 0. (2021)

Step 1: Identify the equation given, which is x² + 6x + 9 = 0.
Step 2: Recognize that this is a quadratic equation in the form ax² + bx + c = 0.
Step 3: Identify the values of a, b, and c from the equation: a = 1, b = 6, c = 9.
Step 4: Use the formula for the product of the roots of a quadratic equation, which is given by c/a.
Step 5: Substitute the values of c and a into the formula: c/a = 9/1.
Step 6: Calculate the result: 9/1 = 9.
Step 7: Conclude that the product of the roots of the equation is 9.

Quadratic Equations – Understanding the standard form of a quadratic equation and how to find the product of its roots using the formula c/a.
Vieta's Formulas – Application of Vieta's formulas to determine relationships between the coefficients of a polynomial and its roots.