What is a real root?

A real root, also known as a real solution or real zero, is a value or number that satisfies a given equation and makes it equal to zero. In other words, it is a value that, when substituted into the equation, results in an equation that holds true.

For example, consider the equation x^2 - 4 = 0. By solving this equation, we can determine its real roots. Factoring the equation, we have (x + 2)(x - 2) = 0. Using the zero product property, we can set each factor equal to zero: x + 2 = 0 and x - 2 = 0. Solving these equations, we find that x = -2 and x = 2. Therefore, -2 and 2 are the real roots of the equation.

Real roots can occur in various types of equations, including polynomial equations, trigonometric equations, exponential equations, logarithmic equations, and more. The number of real roots that an equation can have depends on its degree and the nature of the equation.

Real roots have practical significance in fields such as engineering, physics, and finance. They represent actual values or solutions to real-world problems that can be measured, quantified, or calculated. For example, in finance, real roots can represent the solutions to equations that determine interest rates, investment returns, or debt repayment schedules.

To find real roots, various mathematical methods can be used, including factoring, synthetic division, long division, numerical methods, and graphical methods. These methods help in analyzing equations and determining the real solutions that make the equation equal to zero.