Question

At which root does the graph of f(x) = (x – 5)3(x + 2)2 touch the x axis?

Answer 1

all of them

the roots of thhe equaiton are the x intercept
they would be at x=5 and x=-2

Answer 2

x=5 and x=-2

Explanation:

Knowing that a root is a "x" value where f(x)=0, and consequently the graphic goes through the absise (x axis). We have that when:

f(5)=(5-5)3(5+2)2 =0

and

f(-2)= (-2+5)3(-2+2)2 =0

Then, x=5 and x= -2 are function's roots and the graph touchs the x axis in two "x" values.