Question

Please help:Let f (x) = x^2 − 5x − 36.Enter the x-intercepts of the quadratic function in the boxes. x = __ and x = __

Answer 1

Given

we have a function

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

Required

We need to find its x-intercepts.

Step-by-step explanation

In order to find the x-intercepts we put

`f(x)=0`

i.e.

`\begin{gathered} x^2-5x-36=0 \\ \Rightarrow x^2-9x+4x-36=0 \\ \Rightarrow x(x-9)+4(x-9)=0 \\ \Rightarrow(x-9)(x+4)=0 \\ \Rightarrow x-9=0\text{ or }x+4=0 \\ i.e\text{ }x=9\text{ or }x=-4 \end{gathered}`

so the required x intercepts are x=9 and x=-4.