Question

ach of the following polynomial functions?
b. $f(x)=x^2 - 6x + 9$
hint (b):
the roots are the $x$-intercepts on the graph of the function.

Explanation:

Step1: Factor the quadratic polynomial

We recognize the polynomial as a perfect square trinomial: $x^2 - 6x + 9 = (x-3)^2$

Step2: Find roots by setting to 0

Set $(x-3)^2 = 0$, solve for $x$:
$x-3=0 \implies x=3$
This is a repeated root (multiplicity 2).

Answer:

The root of the polynomial function is $x=3$ (with multiplicity 2, corresponding to an x-intercept at $(3,0)$).