Question

find the zeros of the function. answer in exact form. do not round.
r(x)=-\frac{1}{2}x^{2}-24
the zeros of r are x = and x =

Explanation:

Step1: Set the function equal to zero

$-\frac{1}{2}x^{2}-24 = 0$

Step2: Isolate the $x^{2}$ - term

First, add 24 to both sides: $-\frac{1}{2}x^{2}=24$. Then multiply both sides by - 2 to get $x^{2}=-48$.

Step3: Solve for $x$

Take the square - root of both sides. Since we have $x^{2}=-48$, then $x=\pm\sqrt{-48}$. Simplify $\sqrt{-48}=\sqrt{48}\times\sqrt{-1}=\pm4\sqrt{3}i$.

Answer:

$x = 4\sqrt{3}i$ and $x=-4\sqrt{3}i$