How many real roots does $x ^ { 4 } + 12 x - 5$ have?
Answer is 2. Let $f$ be the given polynomial. Then $f ( 0 )$ is negative and $f$ is positive as $x$ tends to $\pm \infty$. Hence it has at least 2 real roots. Since the derivative of $f$ is zero only at $\sqrt [ 3 ] { - 3 }$, it cannot have more than two real roots.
How many real roots does $x ^ { 4 } + 12 x - 5$ have?