Answer
Zero: $-\dfrac{5}{2}$
$x$-intercept: $-\dfrac{5}{2}$
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 $g(x)=0$:
$$4x^2+20x+25=0$$
Comparing $4x^2+20x+25=0$ to $ax^2+bx+c=0$ to find $a,b \text{ and } c$:
$$\therefore a = 4, b=20 , c =25$$
Evaluating the discriminant $b^2-4ac$
$$b^2-4ac = (20)^2-4 \times 4 \times 25 = 0$$
Since the discriminant is equal to zero, then there is a real repeated root.
The quadratic formula is given by:
$$x= \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$$
$$x= \dfrac{-20\pm \sqrt{0}}{2\times 4}$$
$$x=\dfrac{-20\pm 0}{8}$$
$\therefore x =-\dfrac{5}{2}$
