The problem asks: What is the maximum number of real distinct roots that a quartic equation can have? A quartic equation is a polynomial equation of degree 4.

1. Problem Description

The problem asks: What is the maximum number of real distinct roots that a quartic equation can have? A quartic equation is a polynomial equation of degree

4.

2. Solution Steps

A polynomial equation of degree $n$ has at most $n$ roots (including real and complex roots).

A quartic equation is a polynomial equation of degree

4. Therefore, a quartic equation can have at most 4 roots.

It can have at most 4 real roots, and it can have at most 4 distinct real roots.

An example of a quartic equation with 4 distinct real roots is $(x-1)(x-2)(x-3)(x-4) = 0$.

The roots of this equation are $x = 1, 2, 3, 4$, which are 4 distinct real numbers.

Therefore, the maximum number of real distinct roots that a quartic equation can have is

4.

3. Final Answer

4