Question

Identify the zeros of the graph of the function g(x) = x^3 + 6x^2 + 8x

Answer 1

Given the equation:

$g(x)=x^3+6x^2+8x$

To find the zeros of the graph, we will solve the equation: g(x) = 0

so,

$x^3+6x^2+8x=0$

Factor the equation to find the values of x:

$\begin{gathered} x(x^2+6x+8)=0 \\ x(x+2)(x+4)=0 \\ x=0 \\ or,(x+2)=0\rightarrow x=-2 \\ or,(x+4)=0\rightarrow x=-4 \end{gathered}$

so, the answer will be the zeros of the function are:

$x=\mleft\lbrace-4,-2,0\mright\rbrace$