5th degree polynomial a positive leading coefficient Four extrema The only real zeros are: A zero at x = -5 with a multiplicity

Question

horrorfan [7]

2 years ago

12

5th degree polynomial a positive leading coefficient Four extrema The only real zeros are: A zero at x = -5 with a multiplicity

of 2 A zero at x = 1 domain and range 11 nts)

Mathematics

1 answer:

likoan [24] · Answer 1 · 2024-02-03T03:34:05+03:00

In order to graph the required 5th degree polynomial, you take into account that althoug the polynomial is 5th degree, it only has three real zeros. One of its zeros has mulyiplicity 2. That is, the function only crosses the x-axis two times. Thus, you can draw a graph as the following:

where you can observe that the graph crosses the x-axis in x=-5 and x=1. Furthermore, you can notice the four extrema of the function (yellow points).

The domain of the graph are all reals, that is, the domain is the interval (-∞,∞).

The range are also all reals, (-∞,∞). This is becasue due to all leading coefficents are positive, and the degree is 5th, when x is lower and lower, the function is also lower, and if x a is higher and higher, the function is also higher.