Question

why does a cubic polynomial have at least one real root

Answer 1

$\textit{Polynomial}$
$\textit{Why cubic polynomial have at least one real root?}$

$\textit{Fundamental theorem of Algebra, state that,}$
$\textit{Every non-zero, single-variable, n-degree polynomial with complex}$$\textit{Coefficients has, exactly n complex roots.}$
$\textit{It clearly say that any cubic polynomial will have 3 complex roots,}$
$\textit{Including real roots as imaginary part equal zero.}$

$\textit{For complex roots, it always come with its pair or conjugate,}$
$\textit{Therefore 3-2 = 1 root, which always be Real root.}$

$\textit{By simply looking at odd degree polynomial graph,}$
$\textit{We can see it always cut x-axis no matter what coefficient.}$

Answer 2

Cubic polynomial has 3 roots and the possibilities be two ways
1. 3 roots are real roots
2. One root is real root and the two roots be complex roots (since complex roots are conjugate to one another