1. The problem asks: "All quartic polynomial equations have at least one real solution. True or False?" 2. A quartic polynomial is a polynomial of degree 4, generally written as $$ax^4 + bx^3 + cx^2 + dx + e = 0$$ where $a \neq 0$. 3. According to the Fundamental Theorem of Algebra, every polynomial equation of degree $n$ has exactly $n$ complex roots (counting multiplicities). 4. However, complex roots can be non-real (involving imaginary numbers). Quartic polynomials can have 0, 2, or 4 real roots. 5. For example, the polynomial $$x^4 + 1 = 0$$ has no real roots because $$x^4 = -1$$ has no real solution. 6. Therefore, it is false that all quartic polynomials have at least one real solution. Final answer: False