Answer:
The x-intercepts are (4,0) and (-9,0)
Step-by-step explanation:
We want to find the x-intercepts of the function: [tex]f(x)=x^2+5x-36[/tex]
At x-intercept, [tex]f(x)=0[/tex]
[tex]\implies x^2+5x-36=0[/tex]
We split the middle term to obtain;
[tex]x^2+9x-4x-36=0[/tex]
Factor by grouping:
[tex]x(x+9)-4(x+9)=0[/tex]
[tex](x-4)(x+9)=0[/tex]
Apply the zero product principle.
[tex](x-4)=0,(x+9)=0[/tex]
[tex]x=4,x=-9[/tex]
Hence the x-intercepts are (4,0) and (-9,0)
