at which root does the graph of $f(x) = (x - 5)^3(x + 2)^2$ touch the x-axis?\n-5\n-2\n2\n5

at which root does the graph of $f(x) = (x - 5)^3(x + 2)^2$ touch the x-axis?\n-5\n-2\n2\n5

at which root does the graph of $f(x) = (x - 5)^3(x + 2)^2$ touch the x-axis?\n-5\n-2\n2\n5

Answer

Explanation:

Step1: Identify root multiplicities

For $f(x)=(x-5)^3(x+2)^2$, roots are $x=5$ (multiplicity 3) and $x=-2$ (multiplicity 2).

Step2: Check touch condition

Even multiplicity means graph touches x-axis. $x=-2$ has even multiplicity.

Answer:

-2