What is the product of solutions to a quadratic equation?

The product of the solutions (also known as roots) of a quadratic equation is equal to the constant term divided by the leading coefficient.

Let's elaborate with a general quadratic equation:

General Form of a Quadratic Equation

A quadratic equation is generally expressed as:

ax² + bx + c = 0

Where:

• a, b, and c are constants.
• x is the variable.
• a ≠ 0 (otherwise, it wouldn't be a quadratic equation).

Product of Roots

According to the provided information, the product of the roots of the quadratic equation is calculated as:

Product of Roots = c / a

This means you take the constant term (c) and divide it by the leading coefficient (a).

Example

Consider the quadratic equation:

2x² + 5x + 3 = 0

Here, a = 2, b = 5, and c = 3.

The product of the roots will be:

Product of Roots = 3 / 2 = 1.5

Table Summary

Term	Description
Quadratic Equation	ax² + bx + c = 0
Leading Coefficient	a
Constant Term	c
Product of Roots	c / a