Given:
[tex]f(x)=(x^2+2x)^2-11(x^2+2x)+24[/tex]To find the x-intercept. set f(x)=0 and solve for x
That is;
[tex](x^2+2x)^2-11(x^2+2x)+24=0[/tex]Let
x² + 2x = m
[tex]m^2-11m+24=0[/tex]We can now solve the above quadratic equation;
Using factorisation method;
[tex]m^2-3m-8m+24=0[/tex][tex]m(m-3)-8(m-3)=0[/tex][tex](m-3)(m-8)=0[/tex]Either m-3 = 0 or m-8=0
Either m = 3 or m=8
Recall that;
m= x² + 2x
Substitute m=3 and solve for x
3 = x² + 2x
x² + 2x- 3 =0
or
x² + 2x = 8
