Question

At which root does the graph of f (x) = (x - 5)3 (x + 2)2 touch the xaxis

Answer 1

x=-2

Step-by-step explanation

The given polynomial function is:

`f(x) = {(x - 5)}^(3) {(x + 2)}^(2)`

The polynomial has two factors, one with an odd multiplicity which is

`{(x - 5)}^(3)`

and the other with an even multiplicity which is

`{(x + 2)}^(2)`

The graph does not cross the x-axis at where the multiplicity is even.

Therefore the graph touches the x-axis at

`x = - 2`

We got this by solving

`{(x + 2)}^(2) = 0`