Question

Identify the x-intercept of m(x).
m(x)=x^2-2x-8/x^2-x-2

Answer 1

`\large\boxed{x-intercepts:-2\ and\ 4}`

Explanation:

`m(x)=(x^2-2x-8)/(x^2-x-2)\\\\\text{At the beginning we de}\text{fine the domain:}\\\\D:x^2-x-2\\eq0\\\\x^2-2x+x-2\\eq0\\x(x-2)+1(x-2)\\eq0\\(x-2)(x+1)\\eq0\iff x-2\\eq0\ \wedge\ x+1\\eq0\\\boxed{x\\eq2\ \wedge\ x\\eq-1}\\================================\\\text{The x-intercept is for}\ m(x)=0.\ \text{Therefore we have the equation:}\\\\(x^2-2x-8)/(x^2-x-2)=0\iff x^2-2x-8=0\\\\x^2+2x-4x-8=0\\x(x+2)-4(x+2)=0\\(x+2)(x-4)=0\iff x+2=0\ \vee\ x-4=0\\\\x=-2\in D\ \vee\ x=4\in D`