Question

F(x)= x 2 +12x+20 Enter your answers in the boxes.
What are the zeros

Answer 1

-10 and -2

Explanation:

to find Zeros substitute f(x) to 0

`\displaystyle {x}^(2) + 12x + 20 = 0`

rewrite the middle term as 2x+10x:

`\displaystyle {x}^(2) +2x + 10x+ 20 = 0`

factor out x:

`\displaystyle x ({x}^{} +2)+ 10x+ 20 = 0`

factor out 10:

`\displaystyle x ({x}^{} +2)+ 10(x+ 2) = 0`

group:

`\displaystyle (x + 10)(x+ 2) = 0`

by Zero product property we obtain:

`\displaystyle \begin{cases} x + 10 = 0\\ x+ 2 = 0\end{cases}`

cancel 10 from the first equation 2 from the second:

`\displaystyle \begin{cases} x = - 10\\ x = - 2\end{cases}`

hence, the Zeros of the function are -10 and -2

Answer 2

-10 and -2 are the zeroes

Explanation:

Factor: x^2 + 12x + 20

(x + 10)(x+2)

Set each factor to 0 and solve for x

x + 10 = 0 | x = -10

x + 2 = 0 | x = -2

The zeros are the values for x