Suppose $n \geq 2$. Consider the polynomial $$Q _ { n } ( x ) = 1 - x ^ { n } - ( 1 - x ) ^ { n } .$$ Show that the equation $Q _ { n } ( x ) = 0$ has only two real roots, namely 0 and 1.
Suppose $n \geq 2$. Consider the polynomial
$$Q _ { n } ( x ) = 1 - x ^ { n } - ( 1 - x ) ^ { n } .$$
Show that the equation $Q _ { n } ( x ) = 0$ has only two real roots, namely 0 and 1.