1. The problem is to define what a real root is in mathematics. 2. A real root of an equation is a solution that is a real number. For example, if we have a polynomial equation $f(x) = 0$, a real root is any value of $x$ that satisfies this equation and is a real number. 3. Important rules: - Real roots can be positive, negative, or zero. - Not all equations have real roots; some have complex roots. 4. For example, the equation $x^2 - 4 = 0$ has real roots because it can be factored as $(x-2)(x+2) = 0$, so the roots are $x=2$ and $x=-2$, both real numbers. 5. In summary, a real root is any solution to an equation that lies on the real number line.