Question

Find the zeros of each function by factoring. F(x)=x^2+12x+20.

Answer 1

We need to find the zeros of the function:

`f(x)=x^2+12x+20`

We can represent the equation by a product of its roots. So the first step is to find them.

`\begin{gathered} x_(1,2)=\frac{-12\pm\sqrt[]{(12)^2-4(1)(20)}}{2\cdot1} \\ x_(1,2)=\frac{-12\pm\sqrt[]{144-80}}{2} \\ x_(1,2)=\frac{-12\pm\sqrt[]{64}}{2} \\ x_(1,2)=(-12\pm8)/(2) \\ x_1=(-12-8)/(2)=-10 \\ x_2=(-12+8)/(2)=-2 \end{gathered}`

We can represent the function as:

`f(x)=(x+10)\cdot(x+2)`

The two zeros are the solutions of the equation and are -2 and -10.