Question

What are the x-intercepts of the graph of the function f(x) = x + 5x - 36?

(-4,0) and (9, 0)
(4,0) and (-9.0)
(-3,0) and (12, 0)
(3, 0) and (-12, 0)​

Answer 1

The x-intercepts are (4,0) and (-9,0)

Explanation:

We want to find the x-intercepts of the function:
`f(x)=x^2+5x-36`

At x-intercept,
`f(x)=0`

`\implies x^2+5x-36=0`

We split the middle term to obtain;

`x^2+9x-4x-36=0`

Factor by grouping:

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

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

Apply the zero product principle.

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

`x=4,x=-9`

Hence the x-intercepts are (4,0) and (-9,0)