You find the zeros by solving the equation [tex]\sf{f(x)\:=\:x²\:+\:5x\:+\:6\:=\:0:}[/tex]
[tex]\begin{gathered}\sf \: x = \dfrac{-5\:±\:\sqrt{25\:-\:4\:·\:1\:·\:6}}{2} \\ \\ \sf \: = \dfrac{-5\:±\:\sqrt{25\:-\:24}}{2} \\ \\ \sf \: = \dfrac{-5\:±\:1}{2} \end{gathered}[/tex]
This gives
[tex]\begin{gathered}\sf \: x₁ = \dfrac{-5\:-\:1}{2} = -3, \\ \\ \sf \: x₂ = \dfrac{-5\:+\:1}{2} = -2. \end{gathered}[/tex]
So the graph meets the x-axis in i [tex]\sf{(-3,\:0)}[/tex] and [tex]\sf{(-2,\:0)}[/tex].
[tex]\:[/tex]
Zeros of a Function
The zeros or roots of a function tell us where a graph intersects the x-axis. Since we're talking about intersection with the x-axis, you know that y = 0. That means that you can find the zeros by solving the equation f(x) = 0.
[tex]\:[/tex]
Rule
Zeros
You find the zeros of a function by solving the equation
[tex]\sf{ \: \: \: \: f(x)\:=\:0.}[/tex]
[tex]\:[/tex]
The sign chart of f(x) tells you when the graph of f is above or below the x-axis, and where f(x) intersects the x-axis.
[tex]\:\:\:\:\:\:\:\: \boxed{\sf{See\:the\:picture}}[/tex]
[tex]\:[/tex]
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