Question

What are the zeros of f?f(x) = x² + 5x - 36A) 4 and -9B) -3 and 12C) 3 and 12 D) -4 and 9

Answer 1

Given the function:

`f(x)=x^2+5x-36`

Let's find the zeros of the function.

To find the zeros, substitute 0 for f(x) and solve for x.

We have:

`\begin{gathered} 0=x^2+5x-36 \\ \\ x^2+5x-36=0 \end{gathered}`

Factor the expression using the AC method.

Find a pair of intergers whose sum is 5 and whose product is -36.

We have:

-4 and 9

Thus, we have the factors:

`(x-4)(x+9)=0`

Now, equate each factor to zero and solve for x:

`\begin{gathered} x-4=0 \\ \text{Add 4 to both sides:} \\ x-4+4=0+4 \\ x=4 \\ \\ \\ x+9=0 \\ Subtract\text{ 9 from both sides:} \\ x+9-9=0-9 \\ x=-9 \end{gathered}`

We have the solutions:

x = 4 and -9

Therefore, the zeros of the function are: 4 and -9

ANSWER:

A) 4 and -9