Chapter 4 - Polynomial and Rational Functions - 4.5 The Real Zeros of a Polynomial Function - 4.5 Assess Your Understanding - Page 233: 60

$\{\frac{5}{2} \}$

Step 1. Given $f(x)=2x^3-3x^2-3x-5$, list possible rational zeros as $\frac{p}{q}=\pm1,\pm5,\pm\frac{1}{2},\pm\frac{5}{2}$ Step 2. Use synthetic division as shown in the figure to find a zero $x=\frac{5}{2}$. Step 3. Use the quotient and solve $2x^2+2x+2=0$ and we can not find real solutions. Step 4. Thus the real zeros are $\{\frac{5}{2} \}$