Answers:
- There are 2 unique roots
- The root x = -3 has multiplicity 4
- The root x = 1 has multiplicity 3
- The graph is shown below
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Step-by-step explanation:
The term "zeros" is the same as the term "roots".
The function f(x) = (x+3)^4(x-1)^3 has the roots x = -3 and x = 1
This is because plugging either x value into f(x) leads to f(x) = 0
We can find these roots by setting f(x) equal to 0 and solving for x
So,
f(x) = 0
(x+3)^4(x-1)^3 = 0
(x+3)^4 = 0 or (x-1)^3 = 0
x+3 = 0 or x-1 = 0
x = -3 or x = 1
The root x = -3 occurs with multiplicity 4, since this is the exponent for the factor (x+3). The root x = 1 occurs with multiplicity 3.
Even multiplicity real number roots are visually shown as "parabolic" pieces of a curve that touch at exactly one point on the x axis. Think of a ball bouncing off the floor (it goes down and then bounces back up).
Odd multiplicity real number roots are visually shown as the curve passing through the x axis.