Roots

Let $f(x) = x^7 + 14 x^5 + 17 x^3 + 15x - 22$

$f(0) = -22 < 0$

$f'(x) = 7x^6 + 70 x^4 + 51x^2 + 15 > 0$

For $x > 0, f(x)$ is monotonic increasing for $x \in R.$

$\therefore$ Number of roots = 1, and it is positive since $f(0) < 0.$