Chapter 2 - Linear and Quadratic Functions - Section 2.3 Quadratic Functions and Their Zeros - 2.3 Assess Your Understanding - Page 146: 17

the zeros are $x=-1/2$ or $x=3$ and the $x$-intercepts are $(-1/2,0)$ and $(3,0)$.

By factorization, we have $$ g(x)=2x^2-5x-3=(2x+1)(x-3) .$$ That is, we have $2x+1=0 $ or $x-3=0$. So the zeros are $x=-1/2$ or $x=3$ and the $x$-intercepts are $(-1/2,0)$ and $(3,0)$.