The product of the roots of the equation x^2 + 7x + 10 = 0 is:

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Question: The product of the roots of the equation x^2 + 7x + 10 = 0 is:

Options:

Correct Answer: 10

Solution:

The product of the roots is given by c/a = 10/1 = 10.

The product of the roots of the equation x^2 + 7x + 10 = 0 is:

The product of the roots of the equation x^2 + 7x + 10 = 0 is:

Step 1: Identify the equation given, which is x^2 + 7x + 10 = 0.
Step 2: Recognize that this is a quadratic equation in the form ax^2 + bx + c.
Step 3: Identify the values of a, b, and c from the equation: a = 1, b = 7, c = 10.
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 = 10/1.
Step 6: Calculate the result: 10/1 = 10.
Step 7: Conclude that the product of the roots of the equation is 10.

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.