Question 72
Let $n$ be a positive even integer, and let $c_1, c_2, \dots, c_{n-1}$ be real numbers satisfying
$$
\sum_{i=1}^{n-1} |c_i - 1| \lt 1.
$$
Prove that
$$
2x^n - c_{n-1}x^{n-1} + c_{n-2}x^{n-2} - \dots - c_1x + 2
$$
has no real roots.
$$
\sum_{i=1}^{n-1} |c_i - 1| \lt 1.
$$
Prove that
$$
2x^n - c_{n-1}x^{n-1} + c_{n-2}x^{n-2} - \dots - c_1x + 2
$$
has no real roots.