Answer:
x= -6 and x= 4
Step-by-step explanation:
WE need to find x intercepts for the given quadratic function
[tex]f(x)=x^2+2x-24[/tex]
To find x intercept we set f(x)=0 and solve for x
[tex]0=x^2+2x-24[/tex]
To solve for x we need to factor x^2 +2x-24
We need to find out two factors whose product is -24 and sum is 2
6 times -4= -24 and 6-4= 2
Break the middle term 2x using factors 6x-4x
[tex]0=x^2+6x-4x-24[/tex]
[tex]0=(x^2+6x)+(-4x-24)[/tex]
[tex]0=x(x+6)-4(x+6)[/tex]
0=(x+6)(x-4)
now we set each factor =0 and solve for x
x+6 =0 , so x=-6
x-4=0 so x= 4
x= -6 and x= 4
