Explain Real Roots with Examples.

A real root is a solution to an equation that is also a real number.

Real roots of a polynomial equation are solutions that belong to the set of real numbers. In the context of quadratic equations like ax²+bx+c=0, real roots can be found using the quadratic formula: ​​x = (−b ± b²−4ac)​​/2a.

For example, consider the equation x²−4=0. The coefficients are a = 1, b = 0, and c = −4. Applying the quadratic formula, we get two real roots: x = 2 and x = -2. These roots indicate the points where the quadratic function crosses the x-axis, as the graph intersects the real number line.

On the other hand, the equation x²+2=0 has no real roots, since x² ≥ 0 for any real number x. It does have roots, but they are non-real complex numbers, specifically √2i and -√2i.

In general, a quadratic equation ax²+bx+c=0 has two real roots if the discriminant b²-4ac is positive. If the discriminant is zero, there is only one real solution. If the discriminant is negative, there are no real solutions.