If complex coefficients are allowed, the answer is 3.
If the polynomial must have real coefficients, then each complex root comes as a pair of complex conjugate roots.
Root -5 is real, so that is 1 root, and degree 1.
Root 1 + 4i is complex, so it must come with its complex conjugate, 1 - 4i. This adds 2 roots to the polynomial, and now we're up to degree 3.
Root -4i is also complex. It also must come with its complex conjugate, 4i. That adds two more roots, and the degree is 5.
Answer: The least possible degree is 5 with real coefficients.
Y = (37.50/5)x
y = 7.50x
Graph: Since the graph will start at the origin (0,0) and has a constant rate of $7.50 per hour, the graph will be linear and in proportion. Some cooridinate are as follows:
x: 0 1 2 3 4 5 ....(add 1...)
y: 7.5 15 22.5 30 37.50 45....(add 7.50...)
The trick here is the recognize that the diagonal length of the rectangle is the diameter of the circle.
W = width of rectangle = 4
L = length of rectangle = 3
D = diagonal of rectangle
Using pythagorean theorem, we solve for D.
W^2 + L^2 = D^2
(4)^2 + (3)^2 = D^2
16 + 9 = D^2
25 = D^2
5 = D or -5 = D
Since D is a length, D must be positive. Therefore, D=5.
D = diagonal of the rectangle = 5
Since D is also the diameter of the circle AND the diameter of a circle is twice the radius, we have the following equation :
r = radius of circle = 1/2 D = 1/2 (5) = 2.5
C = circumference
C = 2 pi r = 2 pi (2.5) = 5 pi
