Answer
Zeros: $-1,-\dfrac{3}{2}$
$x$-intercepts: $-1,-\dfrac{3}{2}$
Work Step by Step
To find the zeros of a function $f$, solve the equation $f(x)=0$
The zeros of the function are also the $x-$intercepts.
Let $g(x)=0$:
$$2x^2+5x+3=0$$
Comparing $2x^2+5x+3$ to $ax^2+bx+c=0$ to find $a,b \text{ and } c$
$$\therefore a = 2, b=5 , c =3$$
Evaluating the discriminant $b^2-4ac$
$$b^2-4ac = (5)^2-4 \times 2 \times 3 = 1$$
The quadratic formula is given by:
$$x= \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$$
$$x= \dfrac{-5 \pm \sqrt{1}}{2\times 2}$$
$$x=\dfrac{-5 \pm 1}{4}$$
$\therefore x =-1\hspace{20pt} \text{or} \hspace{20pt} x=-\dfrac{3}{2}$
