Chapter 3 - Polynomial and Rational Functions - Section 3.2 The Real Zeros of a Polynomial Function - 3.2 Assess Your Understanding - Page 224: 64

$x=1$ (multiplicity 2).

Step 1. For $x^4-2x^3+10x^2-18x+9=0$, list possible rational real zeros $\frac{p}{q}: \pm1,\pm2,\pm3,\pm9$ Step 2. Use synthetic division as shown in the figure to find zero(s) $x=1$ (multiplicity 2). Step 3. Use the quotient to find other zeros: $x^2+9=0$, no real solutions.