Question

Which of the following points is an x-intercept of the following graph? f(x)=(x^2+2x)^2-11(x^2+2x)+24

Answer 1

Given:

`f(x)=(x^2+2x)^2-11(x^2+2x)+24`

To find the x-intercept. set f(x)=0 and solve for x

That is;

`(x^2+2x)^2-11(x^2+2x)+24=0`

Let

x² + 2x = m

`m^2-11m+24=0`

We can now solve the above quadratic equation;

Using factorisation method;

`m^2-3m-8m+24=0`
`m(m-3)-8(m-3)=0`
`(m-3)(m-8)=0`

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