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.

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

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.