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

User Sylbru
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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

User TheSprinter
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