What are real roots?

Real roots refer to the solutions of an equation that exist within the set of real numbers. This means that when you solve an equation, if you arrive at a number that can be identified on the real number line—whether it's a whole number, fraction, or irrational number—this is considered a real root.

For instance, if you have a quadratic equation, the roots can be derived using the quadratic formula, and if those roots evaluate to numeric values like 2, -3.5, or √2, these values are classified as real roots. The concept of real roots is crucial in various mathematical applications, especially when considering graphs of functions, where real roots correspond to the x-intercepts.

Imaginary numbers do not fall within the realm of real roots, as they involve the square roots of negative numbers, such as i (the imaginary unit). Non-numeric solutions cannot be well-defined within the context of real roots, since roots are specifically numerical solutions to equations. Complex numbers, which include both real and imaginary parts, also do not qualify as strictly real roots when considered in isolation.

Thus, identifying real roots as the solutions to an equation within real numbers aligns perfectly with the mathematical definitions and properties of real roots.